`3^(x^2) = 7^(6 - x)` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 38 - Precalculus (3rd Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

Given

`3^(x^2) = 7^(6 - x)`

applying logarithmicsĀ  on both sides we get

`ln(3^(x^2))=ln(7^(6 - x))`

=> `x^2 ln(3) = (6-x)ln(7)`

=> `x^2 ln(3) = 6*ln(7) - x* ln(7)`

=> `x^2 ln(3)+x* ln(7)-6*ln(7) =0`

=>on solving we get the value of x as

=> x = `(+- sqrt(ln(7) (24ln(3)+ln(7))) - ln(7))/(ln(9))`

=> `x= 2.4925 or x= -4.2637`

We’ve answered 318,916 questions. We can answer yours, too.

Ask a question