Question 466762
Good so far, took log of both sides
For simplicity sake, when I use log i am using log base 2.
{{{3x + 1 = log (3^(x-2))}}}
From here you need to use the following log property:
{{{log x^n = n*log x}}}
This will get the variable x out of the exponent
{{{3x + 1 = (x-2)log 3}}}
Distribute right side
{{{3x + 1 = xlog 3 - 2log 3}}}
Get x's on left side, constants on right
{{{3x - xlog 3 = -2log 3 - 1}}}
Factor out the x on left, and factor out negative on right
{{{x(3 - log 3) = -(2log 3 + 1)}}}
Divide by (3 - log 3) on both sides
{{{ x = -(2log 3 + 1)/(3 - log 3)}}}
If you use your calculator this is approximately
{{{x = -2.95}}}