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

glamrockqueen7 2021-10-25 Answered
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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Expert Answer

brawnyN
Answered 2021-10-26 Author has 20132 answers
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.
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