Solve for r
r=1
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3\times 3^{r+1}=27
Use the rules of exponents and logarithms to solve the equation.
3^{r+1}=9
Divide both sides by 3.
\log(3^{r+1})=\log(9)
Take the logarithm of both sides of the equation.
\left(r+1\right)\log(3)=\log(9)
The logarithm of a number raised to a power is the power times the logarithm of the number.
r+1=\frac{\log(9)}{\log(3)}
Divide both sides by \log(3).
r+1=\log_{3}\left(9\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
r=2-1
Subtract 1 from both sides of the equation.
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