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Exercise

$3^{0.5x}=81$

Step-by-step Solution

1

Rewrite the number $81$ as a power with base $3$ so that we have exponentials with the same base on both sides of the equation

$3^{0.5x}=3^{4}$
2

If the bases are the same, then the exponents must be equal to each other

$0.5x=4$
3

Eliminate the $0.5$ from the left side, multiplying both sides of the equation by the inverse of $0.5$

$x=4\left(\frac{1}{0.5}\right)$
4

Multiply the fraction and term in $4\left(\frac{1}{0.5}\right)$

$x=8$

Final answer to the exercise

$x=8$

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Similar Questions Solved

$5^x=125$

$3^x=243$

$10^x=25$

$4^x=32$

$4^c=64$

$e^x=0$

$2^{6x+7}=\left(\frac{1}{8}\right)^{1-5x}$

Main Topic: Exponential Equations

Exponential equations are those where the unknown appears only in the exponents of powers of constant bases.

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