# Converting logs formula

• Jun 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: $\displaystyle log b M = \frac{log a M}{log a b}$

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

Thanks!
• Jun 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 $\displaystyle \log_B N$.
• Jun 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: $\displaystyle \log_b M = \frac{\log_a M}{\log_a b}$

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

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

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