Math Help - prove this log

1. prove this log

alright so the question is this:

how do u prove this equation:

log base b times M^k= K times log base b times M

sorry about the writing of the equation, i dunno how to type mathmatically =p

2. Originally Posted by abowlofrice
alright so the question is this:

how do u prove this equation:

log base b times M^k= K times log base b times M

sorry about the writing of the equation, i dunno how to type mathmatically =p
Let $a=log_b(M^k)$, then (assuming $M$ is positive and $k$ is real):

$b^a=M^k$, (definition of $log_b$)

so:

$b^a=(b^{log_b(M)})^k$, (again using the definition of $log_b$).

So:

$a=k.log_b(M)$, (using $(u^v)^w=u^{v.w}$ and $b^a=b^c$ implies $a=c$).

Which is:

$log_b(M^k)=k.log_b(M)$.

RonL

3. thx man, made me one step closer to loving math.... =]