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2\times 3^{k-1}=486
Use the rules of exponents and logarithms to solve the equation.
3^{k-1}=243
Divide both sides by 2.
\log(3^{k-1})=\log(243)
Take the logarithm of both sides of the equation.
\left(k-1\right)\log(3)=\log(243)
The logarithm of a number raised to a power is the power times the logarithm of the number.
k-1=\frac{\log(243)}{\log(3)}
Divide both sides by \log(3).
k-1=\log_{3}\left(243\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
k=5-\left(-1\right)
Add 1 to both sides of the equation.