Write the expression as a sum and/or difference of logarithms. Express powers as factors \log[\frac{x(x+4)}{(x+2)^{5}}], x>0 \log[\frac{x(x+4)}{(x+2)^{5}}]=?

mattgondek4

mattgondek4

Answered question

2021-08-02

Write the expression as a sum and/or difference of logarithms. Express powers as factors.
log[x(x+4)(x+2)5],x>0
log[x(x+4)(x+2)5]=? (Simplify your answer.)

Answer & Explanation

Brittany Patton

Brittany Patton

Skilled2021-08-03Added 100 answers

Step 1
It is required to simplify the given expression:
log[x(x+4)(x+2)5]
Step 2
Apply these properties of logarithm to simplify:
log(ab)=log(a)log(b)
log(ab)=log(a)+log(b)
log(xn)=nlog(x)
Step 3
Now, by using these properties simplify the given expression:
log(x(x+4)(x+2)5)=log(x(x+4))log((x+2)5)
=log(x)+log(x+4)5log(x+2)

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