Question

# Solve the equation. Give the actual solution and approximate the solution to four decimal places. See the earlier example.$3^x=11$

Solution

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Step 1
1 of 2

$3^{x} = 1$

$\log3^{x}=\log(11)$

$x\log3=\log(11)$

$x= \dfrac{\log(11)}{\log3}$

$x=2.1826583386441 \approx 2.1827$

Since both sides cannot have the same base, apply the logarithm.
Apply the law of exponent to break down the exponent on the left.
Simplify and solve for x for the exact value. Round to the fourth decimal place.