Solve for a positive value of x. log_(x)(216)=3 Answer:

Understand the equation: Understand the logarithmic equation. The equation log_(x)(216) = 3 means that x raised to the power of 3 equals 216.Convert to exponential: Convert the logarithmic equation to an exponential equation. Using the definition of a logarithm, we can rewrite the equation as x^3 = 216.Solve for x: Solve for x by taking the cube root of both sides. To find x, we take the cube root of 216, which is x = 216^(1/3).Calculate cube root: Calculate the cube root of 216. The cube root of 216 is 6, because 6^3 = 216.Verify the solution: Verify the solution. We substitute x = 6 back into the original equation to check if it satisfies the equation: log_(6)(216) = 3. Since 6^3 = 216, the equation holds true, confirming that x = 6 is the correct solution.

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Solve for a positive value of
x.

log_(x)(216)=3
Answer:

Solve for a positive value of $x$ . $\newline$ $\log _{x}(216)=3$ $\newline$ Answer:

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Precalculus

Product property of logarithms

Full solution

Q. Solve for a positive value of

x

\newline

\log _{x}(216)=3

\newline

Answer:

Understand the equation: Understand the logarithmic equation. $\newline$ The equation $\log_{x}(216) = 3$ means that $x$ raised to the power of $3$ equals $216$ .
Convert to exponential: Convert the logarithmic equation to an exponential equation. $\newline$ Using the definition of a logarithm, we can rewrite the equation as $x^3 = 216$ .
Solve for x: Solve for x by taking the cube root of both sides. $\newline$ To find $x$ , we take the cube root of $216$ , which is $x = 216^{(1/3)}$ .
Calculate cube root: Calculate the cube root of $216$ . The cube root of $216$ is $6$ , because $6^3 = 216$ .
Verify the solution: Verify the solution. $\newline$ We substitute $x = 6$ back into the original equation to check if it satisfies the equation: $\log_{6}(216) = 3$ . $\newline$ Since $6^3 = 216$ , the equation holds true, confirming that $x = 6$ is the correct solution.