Solve the logarithmic equation for x. 2 log x = log 2 + log(4x − 6)

The idea will be to get one log on each side and then take the antilog of each side.

2log(x)  =  log(x²)    <--  a multiplier goes inside as an exponent

log(2) + log(4x - 6)  =  log[2(4x-6)]   <-- logs are added when numbers are multiplied

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2log(x)  =  log(2) + log(4x - 6)

log(x²)  =  log[2(4x-6)] 

Applying the antilog to both sides:

x²  =  2(4x - 6)

x²  =  8x - 12

x² - 8x + 12  =  0

(x - 6)(x - 2)  =  0

x  =  2    or    x  =  6