How do you solve $ln (x) = 2$ $ln(x)=2$ ?

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Answer 1 · 2018-03-30T22:52:39

$\Rightarrow x = e^{2}$ $=>x = e^2$

$\Rightarrow ln (x) = 2$ $=>ln(x) = 2$

Natural log has a base of $e$ $e$ . More explicitly we can write:

$\Rightarrow {ln}_{e} (x) = 2$ $=>ln_e(x) = 2$

Logarithms have the following form:

$\Rightarrow {log}_{a} (x) = b$ $=>log_a(x) = b$

They also have the property:

$\Rightarrow a^{{log}_{a} (x)} = x$ $=>a^(log_a(x)) = x$

So we can raise both sides of our equation by $e$ $e$ to extract the $x$ $x$ :

$\Rightarrow e^{ln (x)} = e^{2}$ $=>e^(ln(x)) = e^2$

$\Rightarrow x = e^{2}$ $=>x = e^2$

How do you solve ln(x)=2ln(x)=2?