Use the law of exponents to rewrite the following as a sum or difference and without exponent: A) `log_a (x^2/(yz^3))`  B) `log (x/(^3sqrt(1-x)))`

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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a)`log_a (x^2/(yz^3)`

First we will expand the logarithm using the properties.

`==> log_a (x^2/(yz^3))= log_a x^2 - log_a y - log_a z^3`

Now we will use the power property.

`==> log_a (x^2/(yz^3)) = 2log_a x -log_a y -3log z`


b) `log (x/(^3sqrt(1-x))) `

`log (x/(^3sqrt(1-x))) = log x - log ^3sqrt(1-x) `

`= log x - log (1-x)^(1/3) `

`= log x - (1/3) log (1-x)`


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