# Question #611c6

May 27, 2017

The answer is $- 1.1832$.

#### Explanation:

May 27, 2017

Given: ${7}^{x + 2} + {7}^{x} = 5$

Use the property that says addition of exponents is the same as multiplication of the base to each respective exponent:

${7}^{2} {7}^{x} + {7}^{x} = 5$

There is a common factor of ${7}^{x}$ that can be moved outside parentheses:

$\left({7}^{2} + 1\right) {7}^{x} = 5$

Square 7:

$\left(49 + 1\right) {7}^{x} = 5$

$\left(50\right) {7}^{x} = 5$

Divide both sides by 50:

${7}^{x} = \frac{5}{50}$

${7}^{x} = \frac{1}{10}$

Use the base 10 logarithm on both sides:

${\log}_{10} \left({7}^{x}\right) = {\log}_{10} \left(\frac{1}{10}\right) = - 1$

Use the property that brings the exponent outside of a logarithm:

$x {\log}_{10} \left(7\right) = - 1$

$x = - \frac{1}{\log} _ 10 \left(7\right)$