expand using the properties of logarithms: log5 y(x+2)/x^4

- anonymous

expand using the properties of logarithms: log5 y(x+2)/x^4

- chestercat

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- anonymous

when expanding a logarithm when two terms are being multiplied together the sum of the logarithm of the two taken seperately is equal for example log base 5 of x(y) is equal to log base 5 of x + log base 5 of y

- anonymous

when a term is being divided then you use the difference of the log with the same base for example log base 5 of x/y is equal to log base 5 of x - log base 5 of y

- anonymous

does that help?

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## More answers

- anonymous

\[\log5 y(x+2)/x^4 = \log5 y(x+2) - \log5x^4 = \log5y+\log5(x+2) - 4\log5x\]

- anonymous

im so lost

- anonymous

bubbamurphy your answer gets cut off

- anonymous

Sorry the above reply got cut out.
\[\log5y(x+2) - \log5x^4 = \log5y + \log5(x+2) - 4\log5x\]

- anonymous

The righthand side of that last post should be your final answer (assuming by log5 you meant base 5)

- anonymous

and yes then you move the power to the front

- anonymous

as bubbamurphy did

- anonymous

when two or multiple things are being multiplied together in the same log you can separate them with addition when they are being divided then you may use subtraction

- anonymous

i did thankyou

- anonymous

-4log5x is my answer?

- anonymous

the whole left side of the equation that bubbamurphy posted is your completed answer

- anonymous

*right side

- anonymous

sorry

- anonymous

no thankyou allot

- anonymous

no problem any other questions while i am here?

- anonymous

expand the expression: log3(x^-2y^3)

- anonymous

\[\log3(x^(-2y^3) = -2y^3\log3x\]

- anonymous

what is above the first x?

- anonymous

the way that you wrote the problem x was to the power of -2y^3

- anonymous

yes

- anonymous

so if x is to the power of that entire quantity you can move that quantity to the front of the logarithm

- anonymous

quantity meaning -2y^3

- anonymous

that is a parenthesis above the first x

- anonymous

there should be a end parenthesis after the -2y^3

- anonymous

thankyou for your help

- anonymous

No problem. :)

- anonymous

do you have time for more?

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