# prove this log

• Dec 13th 2005, 07:21 PM
abowlofrice
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
• Dec 14th 2005, 12:43 AM
CaptainBlack
Quote:

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 \$\displaystyle a=log_b(M^k)\$, then (assuming \$\displaystyle M\$ is positive and \$\displaystyle k\$ is real):

\$\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
• Dec 15th 2005, 09:33 PM
abowlofrice
thx man, made me one step closer to loving math.... =]