How do you solve $ln \sqrt{x - 8} = 5$ $lnsqrt(x-8)=5$ ?

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Answer 1 · 2017-02-18T08:14:52

$x = e^{10} + 8$ $x=e^10+8$

Exponentiate both sides of the equation:

$e^{ln (\sqrt{x - 8})} = e^{5}$ $e^(ln(sqrt(x-8))) = e^5$

Use the logarithmic rule $e^{ln (x)} = x$ $e^ln(x) = x$ to simplify:

$\sqrt{x - 8} = e^{5}$ $sqrt(x-8) = e^5$

Solve for $x$ $x$ by squaring both sides:

$x - 8 = {(e^{5})}^{2} = e^{10}$ $x-8 = (e^5)^2 = e^10$

Simplify: $x = e^{10} + 8$ $x = e^10+8$

How do you solve ln√x−8=5lnsqrt(x-8)=5?