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

Anish Buchanan 2021-10-29 Answered
Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
\(\displaystyle{6}^{{{x}-{6}}}={\frac{{{1}}}{{{7776}}}}\)

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Expert Answer

Brighton
Answered 2021-10-30 Author has 7945 answers
We know that
\(\displaystyle{6}^{{8}}={7776}\Rightarrow{6}^{{-{5}}}={\frac{{{1}}}{{{7776}}}}\)
If bases are same then power must be equal.
Given equation is
\(\displaystyle{6}^{{{x}-{6}}}={\frac{{{1}}}{{{7776}}}}\)
Using equation we can write as
\(\displaystyle{6}^{{{x}-{6}}}={\frac{{{1}}}{{{7776}}}}\Rightarrow{6}^{{{x}-{6}}}={6}^{{-{5}}}\)
As bases are same powers must be equal so
\(\displaystyle\Rightarrow{x}-{6}=-{5}\)
\(\displaystyle\Rightarrow{x}={1}\)
Hence the equation is solved and the value of x is obtained as 1.
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