# Logarithms Questions

1. Jan 13, 2008

Just a quick check, I've spend hours trying to crack this. Have I gone the right way about it?

1. The problem statement, all variables and given/known data
Solve 5^(x-1)= 4^(1-3x)

2. Relevant equations

3. The attempt at a solution

(x-1)log5 = log4 (1-3x)

xlog5 - log5 = log4 - 3xlog4

xlog5 + 3xlog4= log4 + log 5

x(log5 + 3log4) = log4 + log 5

x= log4 + log 5/(log5 + 3log4)

= 0.519( 3dp)

Many thanks
Matt

2. Jan 13, 2008

### rocomath

Looks correct, and I'm assuming that your actual operation was

$$x=\frac{\log 20}{\log{(5\times4^3)}}$$

3. Jan 13, 2008