How do you solve #ln(x-2)^2=6#?

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Answer 1 · 2016-08-15T06:30:03

We will solve for #x# using the very basic properties of natural logarithms. I'll illustrate it below.

We have, #Ln (x - 2)^2 = 6#

Using the property, #Ln m^n = nLn m#,

We have, #Ln (x - 2)^2 = 6#

#implies 2Ln (x - 2) = 6#
#implies Ln (x - 2) = 3#
#implies x-2 = e^3#

In the last step, we used the concept of inverse of the natural logarithms, # Ln m = n implies m = e^n#

Thus,#x = e^3 + 2#

Where #e# is the base of natural logarithms.