Final answer to the problem
$x=5$
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1
Apply the formula: $x^a=y$$\to x^a=pfgg\left(y,x\right)$, where $x^a=y=3^{\left(x-1\right)}=81$, $a=x-1$, $x=3$, $y=81$ and $x^a=3^{\left(x-1\right)}$
$3^{\left(x-1\right)}=3^{4}$
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$3^{\left(x-1\right)}=3^{4}$
Learn how to solve problems step by step online. Solve the exponential equation 3^(x-1)=81. Apply the formula: x^a=y\to x^a=pfgg\left(y,x\right), where x^a=y=3^{\left(x-1\right)}=81, a=x-1, x=3, y=81 and x^a=3^{\left(x-1\right)}. Apply the formula: a^b=a^c\to b=c, where a=3, b=x-1 and c=4. Apply the formula: x+a=b\to x+a-a=b-a, where a=-1, b=4, x+a=b=x-1=4 and x+a=x-1. Apply the formula: x+a+c=b+f\to x=b-a, where a=-1, b=4, c=1 and f=1.
Final answer to the problem
$x=5$
