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Solve the following logarithm problem for the positive solution for x. log_(x)3=(1)/(3) Answer:

Solve the following logarithm problem for the positive solution for x x .\newlinelog⁡x3=13 \log _{x} 3=\frac{1}{3} \newlineAnswer:

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Quotient property of logarithmsright chevron icon

Full solution

Q. Solve the following logarithm problem for the positive solution for x x .\newlinelog⁡x3=13 \log _{x} 3=\frac{1}{3} \newlineAnswer:
  2. Convert to exponential form: Convert the logarithmic equation to exponential form.\newlineUsing the definition of a logarithm, we can rewrite the equation in exponential form: x13=3x^{\frac{1}{3}} = 3.
  3. Solve for x: Solve for x by raising both sides of the equation to the power of 33. To isolate xx, we raise both sides of the equation to the power of 33, which is the reciprocal of 1/31/3: (x1/3)3=33(x^{1/3})^3 = 3^3.
  4. Simplify the equation: Simplify both sides of the equation.\newlineWhen we raise x13x^{\frac{1}{3}} to the power of 33, the exponents multiply, giving us x13×3=x1=xx^{\frac{1}{3} \times 3} = x^1 = x. On the right side, 333^3 equals 2727. So, we have x=27x = 27.

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