Solve for x 14x 10 92x Write the exact answer using base10

Solve for x. 14^-x + 10 = 9^-2x Write the exact answer using base-10 logarithms.

Solution

log₁₀(14^-x+10) = log₁₀(9^-2x)

(-x+10)*log₁₀(14) = (-2x)*log₁₀(9)

(-x+10)*1,14 = (-2x)*0,95

-1,14x+11,4 = -1,9x

0,76x = -11,4

x=-11,4 / 0,76

x=-15