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

log_(125)x=(2)/(3)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{125} x=\frac{2}{3}$ $\newline$ 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 _{125} x=\frac{2}{3}

\newline

Answer:

Understand the logarithmic equation: Understand the logarithmic equation. $\newline$ The given logarithmic equation is $\log_{125}(x) = \frac{2}{3}$ . This means that $125$ raised to the power of $\frac{2}{3}$ equals $x$ .
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: $125^{\frac{2}{3}} = x$ .
Calculate $125^{\frac{2}{3}}$ : Calculate the value of $125^{\frac{2}{3}}$ . Since $125$ is $5^3$ , we can rewrite $125^{\frac{2}{3}}$ as $(5^3)^{\frac{2}{3}}$ . By the power of a power rule $(a^{m})^{n} = a^{m*n}$ , we get $5^{3*(\frac{2}{3})} = 5^2$ .
Calculate $5^2$ : Calculate $5^2$ . $5^2$ is equal to $25$ . Therefore, $x = 25$ .
Check for positive solution: Check if the solution is positive. $\newline$ Since $25$ is a positive number, it is the positive solution for $x$ .

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