How do you solve $ln \sqrt{x} = 3$ $lnsqrt(x) = 3$ ?

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How do you solve $ln \sqrt{x} = 3$ $lnsqrt(x) = 3$ ?

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Answer 1 · 2018-06-23T19:55:33

Rearrange the expression so its shown as an exponential function.

Explanation:

You probably know that $ln$ $ln$ , or "natural logarithm" for short, has $e$ $e$ as its base. You may also know that a logarithm ${log}_{a} b = x$ $log_a b=x$ can be rewritten as $a^{x} = b$ $a^x=b$ . Let's rewrite the expression using these:

${log}_{e} \sqrt{x} = 3$ $log_e sqrt(x)=3$
$e^{3} = \sqrt{x}$ $e^3=sqrt(x)$

Next, let's square each side to get our answer:

${(e^{3})}^{2} = {(\sqrt{x})}^{2}$ $(e^3)^2=(sqrt(x))^2$
$e^{6} = x \approx 403.43$ $e^6=x~~403.43$

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How do you solve $ln \sqrt{x} = 3$ $lnsqrt(x) = 3$ ?

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