Question

Solve the equation. Give the actual solution and approximate the solution to four decimal places. See the earlier example.

3x=113^x=11

Solution

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Answered 1 year ago
Answered 1 year ago
Step 1
1 of 2

3x=13^{x} = 1

log3x=log(11)\log3^{x}=\log(11)

xlog3=log(11)x\log3=\log(11)

x=log(11)log3x= \dfrac{\log(11)}{\log3}

x=2.18265833864412.1827x=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.

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