Question

How do you solve `2^(x+1) = 3(4^x)`?

Answer 1

`x = 1-(log 3)/log 2`.

Explanation:

Use `(a^m)^n=a^(mn) and a^m/a^n=a^(m-n)`.

`2^(x+1)=3(4^x)=3(2^2)^x=3(2^(2x))`
So, 2^(x+1-2x)=3 or 2^(1-x)+3.
Equating logarithms, `(1-x) log 2=log 3`.
`x=1-(log 3)/log 2`..