Question

EXPAND:

Expand the logarithm fully using the properties of logs. Express the final answer in terms of lo​g x and log y.


log x^5y^2


Here are the answer choices:

A . 5 log x +2 log y

b. 10 log xy

C. 10 log x log y

D. log 5x + log 2y



Explain how you got the answer in Words or either in a mathematical expression!!!

Answer 1

`\displaystyle A) 5\log( {x}^{} ) + 2 \log( {y}^{} )`

Explanation:

we would like to expand the following logarithmic expression:

`\displaystyle \log( {x}^(5) {y}^(2) )`

remember the multiplication logarithmic indentity given by:

`\displaystyle \rm \log( \alpha * \beta ) \iff \log( \alpha ) + \log( \beta )`

so our given expression should be

`\displaystyle \log( {x}^(5) ) + \log( {y}^(2) )`

by exponent logarithmic property we acquire:

`\displaystyle 5\log( {x}^{} ) + 2 \log( {y}^{} )`

hence, our answer is A