Question

Solve using logarithm:
2^(4x+1)=3^x

Answer 1

take logs of both sides

log 2^(4x+1) = log 3^x
use rules of logs
(4x+1)log2 = xlog3
4xlog2 + log2 = xlog3
4xlog2 - xlog3 = -log2
x(4log2 - log3) = -log2
x = -log2/(4log2 - log3)
x = log2/(log3 - 4log2)
= ..

let the button-pushing begin

Answer 2

Thank you!