solve the equation ................5^3x =8^x+1 (round to the nearest thosandth.)?

5^(3x) = 8^(x + 1)
log[5^(3x)] = log[8^(x + 1)]
(3x)log(5) = (x + 1)log(8)
(3x)log(5) = (x)log(8) + log(8)
(3x)log(5) - (x)log(8) = log(8)
x[3log(5) - log(8) = log(8)
x = log(8)/[3log(5) - log(8)]
x = 0.9031/(2.0969 - 0.9031)
x = 0.9031/1.1938
x = 0.756 (rounded to the nearest thousandth)

( 3 x ) log 5 = ( x + 1 ) log 8

( 3 x ) log 5 - x log 8 = log 8

( 3 log 5 - log 8 ) x = log 8

x = log 8 / ( 3 log 5 - log 8 )

x = log 8 / ( 1.194 )

x = 0.756