12^-x+3 = 17^-2x

Question

Solve for x. Write the exact answer using either base-10 or base-e logarithms.

Answer 1

12^(-x+3) = 17^(-2x)

x= about -2.34313

graph it and find the x intercept = the real solution, if any

or take logs and get the same anwer

-x+3 = -2log17/log12 = -2(1.14) = -2.28x

2;28x - x = -3

1.28x = -3

x = -3/1.28 = about -2.34

but if you meant 12^-x+3 = 17^-2x, then no real solution exists, as the graph shows no x intercept