Question #c3090

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Answer 1 · 2016-04-05T03:14:31

#x = 3#

Use the identity

#ln(a) - ln(b) -= ln(a/b)#

Therefore,

#ln(4x) - ln(x-1) = ln((4x)/(x-1))#

#= ln(6)#

Since #ln# is an inverse function, we take the exponential with base #e# on both sides to "undo" the #ln#.

#ln((4x)/(x-1)) = ln(6)#

#e^{ln((4x)/(x-1))} = e^{ln(6)}#

#(4x)/(x-1) = 6#

Simplify the equation

#(4x)/(x-1) = 6#

#(2x)/(x-1) = 3#

#2x = 3(x-1)#

#= 3x - 3#

#0 = x - 3#

#x = 3#