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

log_(6)x=-3
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{6} x=-3$ $\newline$ Answer:

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Product property of logarithms

Full solution

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

x

.

\newline

\log _{6} x=-3

\newline

Answer:

Convert to Exponential Form: Convert the logarithmic equation to its equivalent exponential form. $\newline$ The logarithmic equation $\log_{6} x = -3$ can be rewritten in exponential form as $6$ raised to the power of $-3$ equals $x$ . $\newline$ Calculation: $6^{-3} = x$
Calculate Value: Calculate the value of $6$ raised to the power of $-3$ . $\newline$ To find the value of $6^{-3}$ , we take the reciprocal of $6$ cubed. $\newline$ Calculation: $6^{-3} = \frac{1}{6^3} = \frac{1}{6\times6\times6} = \frac{1}{216}$
Verify Positivity: Verify that the solution is positive. $\newline$ The value we found for $x$ is $\frac{1}{216}$ , which is a positive number.

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