Question

Find all the real solutions to the logarithmic equation
$\ln \left(x\right)=2$

• A. $2$
• B. $2^e$
• C. $1,0$
• D. no real solutions
• E. $e^2$

Answer 1

The correct option is E $e^2$

Let both sides be exponents of the base e. The equation $\ln \left(x\right)=2$ can be rewritten as $e^{\ln \left(x\right)}=e^2$.

By now you should know that when the base of the exponent and the base of the logarithm are the same, the left side can be written $x$. The equation $e^{\ln \left(x\right)}=e^2$ can now be written as $x=e^2$.

Therefore, $x=e^2$.

Hence option E is correct.