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QUESTION

# How do you express log 36 in terms of log 2 and log 3?

log36=2*(log2+log3)

To write this expression in terms of log2 and log3 you first have to write number 36 as a product of powers of 2 and 3.

36=6^2=(2*3)^2

So you can write:

log36=log(2*3)^2

Now you can use the properties of logarythms which say rhat:

1. log a^b=b*loga
2. log(a*b)=loga+logb

After using rule 1 you get:

log(2*3)^2=2*log(2*3)

Now if you use rule 2 you get the final result:

2*log(2*3)=2*(log2+log3)

Now you can write the final answer:

log36=2*(log2+log3)