# How do you solve e^ { 1- 8x } = 7957?

Nov 16, 2016

Using the inverse function ln we convert it to a simple algebraic expression.

#### Explanation:

Using the inverse function ln we convert it to a simple algebraic expression.
ln (e^(1-8x) = ln (7957) (look up ln(7957) or use a calculator)

1-8x = 8.98 ; -8x = 7.98 ; x = -0.9975

CHECK:
${e}^{1 - 8 \cdot - 0.9975} = \left(7957\right)$
${e}^{1 + 7.98} = \left(7957\right)$
${e}^{8.98} = \left(7957\right)$ ; 7942 = 7957 (within error of approximation for 2 significant digits)

Nov 16, 2016

${e}^{1 - 8 x} = 7957$ : Given

$\ln {e}^{1 - 8 x} = \ln 7957$ : Take the natural log of both sides to try to get a step closer to isolating x

$\left(1 - 8 x\right) \ln e = \ln 7957$ : ln e are inverses of each other, which equals 1. Bring the exponent $\left(1 - 8 x\right)$ to the front.

$1 - 8 x = \ln 7957$

$- 8 x = \ln 7957 - 1$ : Subtract 1 to the other side to isolate x

$x = - \frac{\ln 7957 - 1}{8}$ : Divide by 8 to the other side to isolate x