SOLUTION: Can you help me solve this problem to 3 significant digits? 8^(5x)=13^(2x-4) So far I have done (2x-4)log (base 8) 13=5x Thank you!

Question 752963: Can you help me solve this problem to 3 significant digits?
8^(5x)=13^(2x-4)
So far I have done
(2x-4)log (base 8) 13=5x
Thank you!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm going to use natural logs since the base is 'e' (and there's no confusion on what the base is)

8^(5x)=13^(2x-4)

ln(8^(5x))=ln(13^(2x-4))

5x*ln(8)=(2x-4)ln(13)

5x*ln(8)=2x*ln(13)-4ln(13)

5x*ln(8)-2x*ln(13) = -4ln(13)

x(5*ln(8)-2*ln(13)) = -4ln(13)

x = -4ln(13)/(5*ln(8)-2*ln(13))

x = -1.94782524483632 ... Use a calculator to evaluate the right side of the previous step

x = -1.95 ... Round to two decimal places (since you want the answer to 3 sig figs)

So the final answer is x = -1.95
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