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 $\displaystyle a=log_b(M^k)$, then (assuming $\displaystyle M$ is positive and $\displaystyle k$ is real):Originally Posted by abowlofrice
$\displaystyle b^a=M^k$, (definition of $\displaystyle log_b$)
so:
$\displaystyle b^a=(b^{log_b(M)})^k$, (again using the definition of $\displaystyle log_b$).
So:
$\displaystyle a=k.log_b(M)$, (using $\displaystyle (u^v)^w=u^{v.w}$ and $\displaystyle b^a=b^c$ implies $\displaystyle a=c$).
Which is:
$\displaystyle log_b(M^k)=k.log_b(M)$.
RonL