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Mathematics 16 Online
OpenStudy (anonymous):

show that:

OpenStudy (anonymous):

\[\log_mn=\frac{ 1 }{ \log_nm }\]

OpenStudy (anonymous):

@ganeshie8 @dan815 @iambatman

Miracrown (miracrown):

You want help proving this identity? Do you know the change of base rule?

Miracrown (miracrown):

so log base a of b is log b divided by log a

OpenStudy (anonymous):

ok then what

Miracrown (miracrown):

Can you decompose those two into the change of base?

OpenStudy (anonymous):

let me try

Miracrown (miracrown):

okie

OpenStudy (anonymous):

@Miracrown so its \[\log_mn=\log n/\log m\]

Miracrown (miracrown):

right

OpenStudy (anonymous):

how does that become the right side

Miracrown (miracrown):

so now take a look at the other side... 1 / log n of m

Miracrown (miracrown):

a/b = 1 / (b/a), right?

Miracrown (miracrown):

reciprical of the reciprical. Now, 1/(log m / log n), apply the change of base formula - what is log m divided by log n

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