# logarithm equation.

• May 27th 2009, 05:39 AM
scorpion007
logarithm equation.
$\log_{b-1}\frac{n}{b}=p$, where n and p are constants. Solve for b.

Hmmm...

Presumably I'd have to set both sides as the exponent of base (b-1) to eliminate the log. But then I have a cubic, right?
• May 27th 2009, 05:42 AM
mr fantastic
Quote:

Originally Posted by scorpion007
$\log_{b-1}\frac{n}{b}=p$, where n and p are constants. Solve for b.

Hmmm...

Presumably I'd have to set both sides as the exponent of base (b-1) to eliminate the log. But then I have a cubic, right?

$(b - 1)^p = \frac{n}{b} \Rightarrow b(b - 1)^p - n = 0$.

What happens next will depend on the values of p and n.
• May 28th 2009, 04:09 AM
Sampras
Quote:

Originally Posted by mr fantastic
$(b - 1)^p = \frac{n}{p} \Rightarrow b(b - 1)^p - n = 0$.

What happens next will depend on the values of p and n.

$(b-1)^{p} = \frac{n}{b}$.