Answer to Question #194734 in Algebra for kmy

Question

Solve the valid solutions of the following equations providing your values for some of them. Write your answers in solution set form. Identify the extraneous solution, if there is.

a^x-1 = b^3-x

(provide values for a and b which are different integers greater than 1)

Answer 1

$a^{x-1}=b^{3-x}$

$\ln a*(x-1)=\ln b* (3-x)$

$x=\frac{3\ln a+\ln b}{\ln a+\\ln b}$

For a=2, b=4:

$x=\frac{3\ln 2+\ln 4}{\ln 2+\\ln 4}=\frac{5\ln 2}{3\ln 2}=\frac{5}{3}$