# How do you solve (e^(x+5) / e^(5)) = 3?

May 23, 2018

Solution: $x = 1.0986$

#### Explanation:

${e}^{x + 5} / {e}^{5} = 3 \mathmr{and} \frac{{e}^{x} \cdot \cancel{{e}^{5}}}{\cancel{{e}^{5}}} = 3$ or

${e}^{x} = 3$ Taking natural log on both sides we get,

$x \ln e = \ln 3 \mathmr{and} x = \ln 3 \left[\ln e = 1\right] \therefore x \approx 1.0986 \left(4 \mathrm{dp}\right)$

Solution: $x = 1.0986$ [Ans]

Jun 8, 2018

$x \approx 1.10$

#### Explanation:

On the left side, we have the same bases, so we can subtract the exponents.

$\left({e}^{\textcolor{red}{\left(x + 5\right)}} / \left({e}^{\textcolor{b l u e}{5}}\right)\right) = {e}^{\textcolor{red}{x + 5} - \textcolor{b l u e}{5}} = \textcolor{\mathrm{da} r k b l u e}{{e}^{x}}$

We now have the equation

${e}^{x} = 3$

The natural log ($\ln$) function cancels with base-$e$, so we can take the natural log of both sides. We get

$\cancel{\ln} {\cancel{e}}^{x} = \ln 3$

$\implies x = \ln 3$

$x \approx 1.10$

Hope this helps!