Solve for X using base-10 logarithms

Question

8^-2x=3^x-10

Help please! :)

Answer 1

8^-2x = 3^{x - 10}

-2x log 8 = (x - 10) log 3

-2x log 8 = x log 3 - 10 log 3

-2x log 8 - x log 3 = -10 log 3

x(-2 log 8 + log 3) = -10 log 3

x = [-10 log 3] / (-2 log 8 + log 3)