DrippQueenMo
Answered

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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!!!

Sagot :

Nayefx

Answer:

[tex] \displaystyle A) 5\log( {x}^{} ) + 2 \log( {y}^{} ) [/tex]

Step-by-step explanation:

we would like to expand the following logarithmic expression:

[tex] \displaystyle \log( {x}^{5} {y}^{2} ) [/tex]

remember the multiplication logarithmic indentity given by:

[tex] \displaystyle \rm \log( \alpha \times \beta ) \iff \log( \alpha ) + \log( \beta ) [/tex]

so our given expression should be

[tex] \displaystyle \log( {x}^{5} ) + \log( {y}^{2} ) [/tex]

by exponent logarithmic property we acquire:

[tex] \displaystyle 5\log( {x}^{} ) + 2 \log( {y}^{} ) [/tex]

hence, our answer is A

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