# Solve the following exponential equation by expressing each side as a power of t

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
$$\displaystyle{2}^{{{7}-{x}}}={\frac{{{1}}}{{{4}}}}$$

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brawnyN
Given:
$$\displaystyle{2}^{{{7}-{x}}}={\frac{{{1}}}{{{4}}}}$$
Calculation:
$$\displaystyle{2}^{{{7}-{x}}}={\frac{{{1}}}{{{4}}}}$$
$$\displaystyle{2}^{{{7}-{x}}}={\frac{{{1}}}{{{2}^{{2}}}}}$$
$$\displaystyle{2}^{{{7}-{x}}}={2}^{{-{2}}}$$
equating exponent
$$\displaystyle{7}-{x}=-{2}$$
$$\displaystyle{7}+{2}={x}$$
$$\displaystyle{x}={9}$$
The solution set is 9.