How do you solve #lnsqrt(x-8)=5#?

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Answer 1 · 2017-02-18T08:14:52

#x=e^10+8#

Exponentiate both sides of the equation:

#e^(ln(sqrt(x-8))) = e^5#

Use the logarithmic rule #e^ln(x) = x# to simplify:

#sqrt(x-8) = e^5#

Solve for #x# by squaring both sides:

#x-8 = (e^5)^2 = e^10#

Simplify: #x = e^10+8#