Solve the exponential equation 3^x=81 by expressing each side as a power of t

ankarskogC 2021-09-28 Answered

Solve the exponential equation \(3^x=81\) by expressing each side as a power of the same base and then equating exponents.

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Expert Answer

pierretteA
Answered 2021-09-29 Author has 15590 answers
Given:
\(\displaystyle{3}^{{x}}={81}\)
We can write,
\(\displaystyle{81}={3}\times{9}\)
\(\displaystyle={3}\times{3}\times{3}\)
\(\displaystyle\therefore{81}={3}^{{3}}\)
Therefore, we have
\(\displaystyle{3}^{{x}}={3}^{{3}}\)
Using, if \(\displaystyle{a}^{{m}}={a}^{{n}},{a}\ne{0}\) then m=n, we get
x=3
Thus, the solution of the equation \(\displaystyle{3}^{{x}}={81}\) is x=3
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