solve for x

Question

Solve 5^(7x+11) = 8^2x

Answer 1

The equation

5^(7x+11)   =   8^2x

Apply logorithm on each side

log [ 5^(7x+11) ]  =   log [ 8^2x ]

(7x + 11) log 5  =   2x log 8

7x log 5 + 11 log 5  =   2x log 2^3

7x log 5 + 11 log 5  =   3(2x) log 2

7x log 5 - 6x log 2   =   - 11 log 5

x [ 7 log 5 - 6 log 2 ]   =   - 11 log 5

x   =   [ - 11 log 5 ] / [ 7 log 5 - 6 log 2 ]

x   =   [ log 5^-11 ] / [ log 5^7 - log 2^6 ]

x   =   [ log (1/5^11) ] / [ log (5^7)/(2^6) ]