If 3x = 4x-1, then x is equal to

3x = 4x - 1
Taking log on both sides with base 2
xlog₂(3) = (x - 1)log₂(4)
xlog₂(3) = xlog₂(4) - log₂(4)
log₂(4) = x[log₂(4) - log₂(3)]
x = log₂(4) / [log₂(4) - log₂(3)]
x = 2 / [2 - log₂(3)] (∵logₐaˣ = x)
Now using, logₐb = logₓb / logₓa
x = 2 / [2 - log₂(3)]
Dividing by log(3) to numerator and denominator.
x = 2log₃2 / [2log₃2 - 1]
x = 2 / (2 - log₂3) (from 1)
x = 2 / (2 - log₂3) = 1 / (1 - log₂3 /2)
x = 1 / (1 - log₄3) = 1 - log₄3
Alternatively:
3x = 4x-1
3x = 4x / 4
log3x = log(4x/4)
xlog3 = xlog4 - log4
x(log4-log3) = log4
x = log4/(log4-log3) = log4/log(4/3) = log₄(4/3)
x = 1 - log₄3