Solving Logarithms Questions - Matt's Attempt

[monkeyhead]

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

Homework Statement

Solve 5^(x-1)= 4^(1-3x)

Homework Equations

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

 

[rocomath]

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

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

 

[monkeyhead]

I see thanks for the feedback
Matt

 

[rocomath]

If you have a TI, just store your answer and then plug it back into your original equation and see if L=R.