Question 9767
Using logarithms:

{{{Log(3.45^x) = Log(8)}}} 

{{{xLog(3.45) = Log(8)}}} Divide both sides by Log(3.45)

{{{x = (Log8)/Log 3.45}}}

{{{x = 1.67917055245}}}

Check; Using a calculator:

{{{3.45^1.67917055245 = 8.00000000001}}}