How do you solve Ln(x)-2=0?

Jun 19, 2016

$x = {e}^{2}$

Explanation:

A logarithm ${\log}_{a} \left(x\right)$ is the value fulfilling the equation ${a}^{{\log}_{a} \left(x\right)} = x$.

$\ln$ represents the natural logarithm, that is, the logarithm with base $e$. To solve, then, we can isolate $\ln \left(x\right)$ and then apply the exponential function. As $\ln \left(x\right)$ is the same as ${\log}_{e} \left(x\right)$, then ${e}^{\ln} \left(x\right) = x$.

$\ln \left(x\right) - 2 = 0$

$\implies \ln \left(x\right) = 2$

$\implies {e}^{\ln \left(x\right)} = {e}^{2}$

$\implies x = {e}^{2}$