What is the solution of the exponential equation 9^(6 - x) - 8^x=0?

The equation 9^(6 - x) - 8^x=0 has to be solved for x.
Here, it is only possible to find the solution as an expression involving logarithm as
it is not possible to equate either the base or the
exponent.

9^(6 - x) -
8^x=0

9^(6 - x) = 8^x

Take the
log of both the sides

log(9^(6 - x)) =
log(8^x)

Use the property log a^b = b*log
a

(6 - x)*log 9 = x*log
8

Isolate x to one side

6*log
9 - x*log 9 = x*log 8

x*(log 8 + log 9) = 6*log
9

x*log 72 = 6*log 9

x =
(6*log 9)/log 72

The solution of the equation 9^(6 - x) -
8^x=0 is x = (6*log 9)/log 72