precalculus question ? anyone help ?
i had a question on my math test today and i couldnt figure it out . i was wondering if anyone could show me how it is solved ?
this is it:
3^(x-1) = 5^x
note* this was a multiple choice question and all the answers had a natural log (ln) in them
any help at all would be greatly appreciated
- 9 years agoFavorite Answer
We are asked to solve: 3^(x - 1) = 5^x. First we have to take the natural logarithm of both sides of the equations and apply the properties of logarithms. Recall
ln(xy) = ln(x) + ln(y)
ln(x/y) = ln(x) - ln(y)
ln(x^y) = y ln(x)
ln(3^(x - 1)) = ln(5^x)
(x - 1) ln(3) = x ln (5)
x ln(3) - ln(3) = x ln (5)
x ln(3) - x ln(5) = ln(3)
x (ln(3) - ln(5)) = ln(3)
x = ln(3) / (ln(3) - ln(5)) = -2.15066
Hope all this helps.