Solve the exponential equation

Question

6^(4x - 2) = 11^(X + 2)

Answer 1

6^(4x - 2)   =   11^(X + 2)

Apply logorithm to each side

log[6^(4x - 2)]   =   log[11^(X + 2)]

(4x - 2) log 6   =   (x + 2) log 11

(4x) log 6 - 2 log 6   =   x log 11+ 2 log 11

(4x) log 6 - x log 11   =   2 log 11 + 2 log 6

x[ 4 log 6 -  log 11]   =    log (11^2) +  log (6^2)

x[ log 1296 -  log 11]   =    log (121 * 36)

x[ log (1296/11)]   =    log 4356

x   =    [ log (4356) ] / [ log (1296/11)]