Solving expotential equation

Question

how to solve the following equation for x

 

4(7^x+2)=9^2x-3

 

Answer 1

Assuming that the equation is 4(7^x+2) = 9^2x-3, 

 

Take log of both sides to get:  log[4(7^x+2)] = log(9^2x-3)

 

log4 + log(7^x+2) = log(9^2x-3)

 

(2x-3)log9 - (x+2)log7 = log4

 

2xlog9 - xlog7 = log4 + 3log9 + 2log7

 

x(2log9-log7) = log4 + log729 + log49

 

x(log81 - log7) = log142884

 

x = log(142884)/(log81-log7) ≈ 4.85