Question

Which is the solution to 5^x=8^x-7

a. 18.6667
b. 15.4851
c. 30.9702
d. –3.9459
Please select the best answer from the choices provided A B C D

Answer 1

C) 30.9702

Explanation:

Take log of both sides:

In5^x = In8^x - 7

Rewrite it using the laws of log:

xIn5 = (x - 7)In8

x / (x - 7) = ln 8 / ln 5

x / (x - 7) = 1.292

x = 1.292x - 9.044

1.292x - x = 9.044

x = 9.044 / 0.292

Thus, x = 30.9702