# How do you solve -8.7e^(6.6-6x)-7=-32.8?

Aug 4, 2016

$x = 0.9188$

#### Explanation:

Let us rewrite the given eqn., by removing all $- v e$ signs, as

$8.7 {e}^{6.6 - 6 x} + 7 = 32.8$

$\Rightarrow 8.7 {e}^{6.6 - 6 x} = 25.8$

$\Rightarrow {e}^{6.6 - 6 x} = \frac{25.8}{8.7}$

$\Rightarrow {\log}_{10} \left\{{e}^{6.6 - 6 x}\right\} = {\log}_{10} 25.8 - {\log}_{10} 8.7$

$\Rightarrow \left(6.6 - 6 x\right) {\log}_{10} e = 1.4116 - 0.9395 = 0.4721$

$\Rightarrow \left(6.6 - 6 x\right) \left(0.4343\right) = 0.4721$

$\Rightarrow \left(6.6 - 6 x\right) = \frac{0.4721}{0.4343} = 1.087$

$\Rightarrow \frac{6.6 - 1.087}{6} = x = 0.9188$.