If x=\log_{12}27,then what is the the value of \log_616?

livinglife100s8x

livinglife100s8x

Answered question

2022-04-27

If x=log1227,then what is the the value of log616?

Answer & Explanation

kubistiedt

kubistiedt

Beginner2022-04-28Added 17 answers

x=log12(27)=3log12(3)
1x=131log12(3)=13log3(12)=13log3(3×4)=13(1+2log3(2))
Simplifying, we get log3(2)=32x12
Let y=log6(16)=4log6(2)=41log2(6)=41+log2(3)
Now make use of the fact that log3(2)=1log2(3) to get y in terms of x.
I get y=4(3x3+x)

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