How to simply this logarithmic equation? I have f ( L ) = M <mrow c

Finley Mckinney

Finley Mckinney

Answered question

2022-06-14

How to simply this logarithmic equation?
I have
f ( L ) = M L 1 / ( M + 1 ) L
and
L = log M ( ( K + B ) / A )
I am suppose to simply this to
f = C ( K + B ) b
with
b = ln ( M + 1 ) ln ( M )
for the top I have simplified M L 1 to K + B A M , but I have no idea how to simplify the bottom part. Some help would be great

Answer & Explanation

Marlee Norman

Marlee Norman

Beginner2022-06-15Added 18 answers

Something like
a log a x
is easy to simplify, this is what you have done for the top line. For the bottom you need to simplify
a log b x   .
Try this:
a log b x = ( b log b a ) log b x = b ( log b a ) ( log b x ) = ( b log b x ) log b a = x log b a   .
I think this will give you what you want.

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