`2^x = 3^(x + 1)` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 35 - Precalculus (3rd Edition, Ron Larson).
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kspcr111 | In Training Educator

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Given

`2^x = 3^(x+1)`

applying logarithmic on both sides we get

`x*ln(2) = (x+1)ln(3)`

`ln(2)/ln(3) = (x+1)/x`

`ln(2)/ln(3) = 1+ 1/x`

`ln(2)/ln(3) -1 = 1/x`

`(ln(2) - ln(3))/ln(3) = 1/x`

`x = ln(3) /(ln(2) - ln(3))`

`= - 2.7095`

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