Question

How do you solve `(0.3)^(1 + x) = 1.7^(2x - 1)`?

Answer 1

`x=(log 1.7+log 0.3) /(2 log 1.7 - log 0.3)=-0.2973`, nearly..

Explanation:

`log a^m=m log a`
Here, `(0.3)^(1+x)=(1.7)^(2x-1)`
Equating logarithms.
`(1+x) log 0.3=(2x-1) log 1.7`

Solving for x.
`x=(log 1.7+log 0.3) /(2 log 1.7 - log 0.3)`