When simplifying exponents, you use basic and simple rules: For multipying, you add the exponents, but in adding and subtracting you keep the exponent the same. Examples: 1) (x^3)(x^4) = x^(3+4) = x^7 2) (x/y)^2 =(x^2/y^2) 3) x^2 + 3x^4 + 2x^2 = 3x^2 + 3x^4
When simplifying logarithms, there are more basic rules for them. Multiplication inside the log is turned into addition outside the log. Division inside the log is turned into subtraction outside the log. And an exponent on the inside of a log is moved out to the front and multiplied. Examples: 1) logb(mn) = logb(m) + logb(n) 2) logb(m/n) = logb(m) – logb(n) 3) logb(m^n) = n X logb(m)
When you are trying to simplify exponents it depends on what the equation is telling you to do. If the equation is addition or subtraction the exponent does not change but when you multiply the exponents get added and if there parentheses the exponents get multiplied together. Examples: x² + x² = 2x² (x²)(x²) = x^4 (x²)³ = x^6 When you have to simplify logarithms you have to follow certain rules. When you want to expand a logarithm, multiplication is represented by addition and division is represented by subtraction. When you are given a logarithm and they don’t want you to expand or condense a logarithm, you can Rewriting in exponential form you take the number that comes after the log and make it the base and take what it is equal to and make that the exponent and take the number after the first and make that equal to the new equation.
When simplifying exponents you use simple algebra. If your adding terms the exponents stay the same, the number in front is the only thing that changes. If you are multiplying terms then you simply add the the exponents together to get your answer.
Ex.
x^3 + x^2 + 4x^3 = 5x^3 + x^2 x^2(x^5) = x^7
When simplifying logarithms multiplication in the log is turned into addition outside of the log. Division is turned into subtraction outside the log. And an exponent on the inside of a log is moved out to the front and multiplied.
for exponents if you add or subtract them the only number that changes is the number in front.
if you multiply the exponents are added together but if you divide they are subtracted.
and if there are parentheses involved the exponents are multiplied together.
when condensing a log you have to remember that if you add it goes at the top but if you subtract it goes to the bottom.
and the same for expanding except the logs will start off as with them either on the top or bottom and you have to realize which is subtraction and which is addition.
Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 53. The "exponent", being 3 in this example, stands for however many times the value is being multiplied. The thing that's being multiplied, being 5 in this example, is called the "base".
This process of using exponents is called "raising to a power", where the exponent is the "power". The expression "53" is pronounced as "five, raised to the third power" or "five to the third". There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed". So "53" is commonly pronounced as "five cubed".
When we deal with numbers, we usually just simplify; we'd rather deal with "27" than with "33". But with variables, we need the exponents, because we'd rather deal with "x6" than with "xxxxxx".
Logarithms, or "logs", are a way of expressing one number in terms of a "base" number that is raised to some power. Common logs are done with base ten, but some logs ("natural" logs) are done with the constant "e" (2.718 281 828) as their base. The log of any number is the power to which the base must be raised to give that number.
The rules for exponents are fairly simple and easy to use in MOST cases, but they can get tricky too. When multiplying bases that have exponents, you simply multiply the bases and add the exponents:
ex: 2^3 x 5^2 = 10 ( 2 x 5 ) ^5 ( 3 + 2 ) so 10^5
When you are dividing bases with exponents, it works the same way, except you DIVIDE the bases and SUBTRACT the exponents:
ex: 10^4 / 2^2 = ( 10 / 2 ) ^( 4 - 2 ) 5^2
Another rule is that when there are two or more exponents but only one base, multiply the exponents:
ex: (x^3)^4 = x^12
And the last and most simple rule is that you can only add or subtract bases with exponents if the exponents match. This means that you can only add squared terms with squared terms and so on. And when you do this, the exponents stay the same.
Rules for logs:
1) Multiplication inside the log can be turned into addition outside the log, and vice versa.
2) Division inside the log can be turned into subtraction outside the log, and vice versa.
3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.
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ReplyDeleteWhen simplifying exponents, you use basic and simple rules: For multipying, you add the exponents, but in adding and subtracting you keep the exponent the same.
ReplyDeleteExamples:
1) (x^3)(x^4)
= x^(3+4)
= x^7
2) (x/y)^2
=(x^2/y^2)
3) x^2 + 3x^4 + 2x^2
= 3x^2 + 3x^4
When simplifying logarithms, there are more basic rules for them. Multiplication inside the log is turned into addition outside the log. Division inside the log is turned into subtraction outside the log. And an exponent on the inside of a log is moved out to the front and multiplied.
Examples:
1) logb(mn) = logb(m) + logb(n)
2) logb(m/n) = logb(m) – logb(n)
3) logb(m^n) = n X logb(m)
When you are trying to simplify exponents it depends on what the equation is telling you to do. If the equation is addition or subtraction the exponent does not change but when you multiply the exponents get added and if there parentheses the exponents get multiplied together.
ReplyDeleteExamples:
x² + x² = 2x²
(x²)(x²) = x^4
(x²)³ = x^6
When you have to simplify logarithms you have to follow certain rules. When you want to expand a logarithm, multiplication is represented by addition and division is represented by subtraction. When you are given a logarithm and they don’t want you to expand or condense a logarithm, you can Rewriting in exponential form you take the number that comes after the log and make it the base and take what it is equal to and make that the exponent and take the number after the first and make that equal to the new equation.
When simplifying exponents you use simple algebra. If your adding terms the exponents stay the same, the number in front is the only thing that changes. If you are multiplying terms then you simply add the the exponents together to get your answer.
ReplyDeleteEx.
x^3 + x^2 + 4x^3 = 5x^3 + x^2
x^2(x^5) = x^7
When simplifying logarithms multiplication in the log is turned into addition outside of the log. Division is turned into subtraction outside the log. And an exponent on the inside of a log is moved out to the front and multiplied.
Here are the three different ways of doing logs:
log(mn) = lo(m) + log(n)
log(m/n) = log(m) – log(n)
log(m^n) = n log(m)
for exponents if you add or subtract them the only number that changes is the number in front.
ReplyDeleteif you multiply the exponents are added together but if you divide they are subtracted.
and if there are parentheses involved the
exponents are multiplied together.
when condensing a log you have to remember that if you add it goes at the top
but if you subtract it goes to the bottom.
and the same for expanding except the logs will start off as with them either on the
top or bottom and you have to realize
which is subtraction and which is
addition.
Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 53. The "exponent", being 3 in this example, stands for however many times the value is being multiplied. The thing that's being multiplied, being 5 in this example, is called the "base".
ReplyDeleteThis process of using exponents is called "raising to a power", where the exponent is the "power". The expression "53" is pronounced as "five, raised to the third power" or "five to the third". There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed". So "53" is commonly pronounced as "five cubed".
When we deal with numbers, we usually just simplify; we'd rather deal with "27" than with "33". But with variables, we need the exponents, because we'd rather deal with "x6" than with "xxxxxx".
Logarithms, or "logs", are a way of expressing one number in terms of a "base" number that is raised to some power. Common logs are done with base ten, but some logs ("natural" logs) are done with the constant "e" (2.718 281 828) as their base. The log of any number is the power to which the base must be raised to give that number.
The rules for exponents are fairly simple and easy to use in MOST cases, but they can get tricky too. When multiplying bases that have exponents, you simply multiply the bases and add the exponents:
ReplyDeleteex: 2^3 x 5^2 = 10 ( 2 x 5 ) ^5 ( 3 + 2 ) so 10^5
When you are dividing bases with exponents, it works the same way, except you DIVIDE the bases and SUBTRACT the exponents:
ex: 10^4 / 2^2 = ( 10 / 2 ) ^( 4 - 2 ) 5^2
Another rule is that when there are two or more exponents but only one base, multiply the exponents:
ex: (x^3)^4 = x^12
And the last and most simple rule is that you can only add or subtract bases with exponents if the exponents match. This means that you can only add squared terms with squared terms and so on. And when you do this, the exponents stay the same.
Rules for logs:
1) Multiplication inside the log can be turned into addition outside the log, and vice versa.
2) Division inside the log can be turned into subtraction outside the log, and vice versa.
3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.