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

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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pierretteA
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