# Converting logs formula

• June 9th 2011, 10:01 AM
elieh
Converting logs formula
Could someone please explain why we use a conversion formula for solving logs which are not of base 10 or e.

I don't understand what the formula is or where it comes from.

Formula: $log b M = \frac{log a M}{log a b}$

How can I also use latex to make something "the base"

Thanks!
• June 9th 2011, 10:21 AM
Plato
Quote:

Originally Posted by elieh
How can I also use latex to make something "the base"

$$\log_B N$$ gives $\log_B N$.
• June 9th 2011, 10:45 AM
Plato
Quote:

Originally Posted by elieh
I don't understand what the formula is or where it comes from.

Formula: $\log_b M = \frac{\log_a M}{\log_a b}$

Let $T=\log_b (M)$ then $M=b^T$.

From which we get $\log_a(M)=T\log_a(b)$

Solve for $T$.
• June 9th 2011, 10:50 AM
elieh
Calculation error
• June 9th 2011, 10:53 AM
elieh
$\log_a b^x = \log_a M$
$x\log_a b =\log_a M$
$x= \frac{\log_a M}{\log_a b}$