Question

Find all the real solutions to the exponential equation
$e^{3x}=-1$

• A. no real solutions
• B. $\ln (-1)/3$
• C. $-1/\ln \left(3\right)$
• D. $0$
• E. $e^{-1},3$

Answer 1

The correct option is A no real solutions

Let both sides be exponents of the base e. The equation $e^{3x}=-1$ can be rewritten as $\ln (-1)=\ln \left(e^{3x}\right)$ .

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 $\ln (-1)=\ln \left(e^{3x}\right)$ can now be written as $3x=\ln (-1)$ or $x=\ln (-1)/3$ .

Therefore, there are no real solution of the given exponential function.

Hence option A is correct.