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Solve the following logarithm problem for the positive solution for
x.

log_(x)10=(1)/(3)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{x} 10=\frac{1}{3}$ $\newline$ Answer:

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Quotient property of logarithms

Full solution

Q. Solve the following logarithm problem for the positive solution for

x

.

\newline

\log _{x} 10=\frac{1}{3}

\newline

Answer:

Understand the logarithmic equation: Understand the logarithmic equation. $\newline$ The given equation is $\log_x(10) = \frac{1}{3}$ , which means we are looking for a base $x$ such that $x$ raised to the power of $\frac{1}{3}$ equals $10$ .
Convert to exponential form: Convert the logarithmic form to exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation in its exponential form: $x^{\frac{1}{3}} = 10$ .
Solve for x: Solve for x. $\newline$ To find $x$ , we need to raise both sides of the equation to the power of $3$ to get rid of the fractional exponent: $(x^{(1/3)})^3 = 10^3$ .
Calculate x value: Calculate the value of x. Raising both sides to the power of $3$ , we get $x = 10^3$ .
Compute $10^3$ : Compute $10^3$ . $\newline$ $10^3$ is $10 \times 10 \times 10$ , which equals $1000$ .

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