Condense each expression to a single logarithm. 2log_(6)u-8log_(6)v

Identify Properties: Identify the properties of logarithms that can be used to condense the expression. The expression involves coefficients in front of the logarithms, which suggests the use of the power property of logarithms to move the coefficients inside the logarithms as exponents. Power Property: a*log_b(P) = log_b(P^a)Apply Power Property: Apply the power property to move the coefficients inside the logarithms as exponents. Using the power property, we can rewrite the expression as follows: 2log_(6)u = log_(6)(u^2) 8log_(6)v = log_(6)(v^8)Combine Using Quotient Property: Combine the two logarithms into a single logarithm using the quotient property. Quotient Property: log_b(P) - log_b(Q) = log_b(P/Q) So, log_(6)(u^2) - log_(6)(v^8) = log_(6)(u^2/v^8)Write Final Answer: Write the final answer as a single logarithm. The expression is now condensed to a single logarithm: log_(6)(u^2/v^8)

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Condense each expression to a single logarithm.

2log_(6)u-8log_(6)v

Condense each expression to a single logarithm. $\newline$ $2 \log _{6} u-8 \log _{6} v$

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Algebra 2

Product property of logarithms

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Q. Condense each expression to a single logarithm.

\newline

2 \log _{6} u-8 \log _{6} v

Identify Properties: Identify the properties of logarithms that can be used to condense the expression. $\newline$ The expression involves coefficients in front of the logarithms, which suggests the use of the power property of logarithms to move the coefficients inside the logarithms as exponents. $\newline$ Power Property: $a\log_b(P) = \log_b(P^a)$
Apply Power Property: Apply the power property to move the coefficients inside the logarithms as exponents. $\newline$ Using the power property, we can rewrite the expression as follows: $\newline$ $2\log_{6}u = \log_{6}(u^2)$ $\newline$ $8\log_{6}v = \log_{6}(v^8)$
Combine Using Quotient Property: Combine the two logarithms into a single logarithm using the quotient property. $\newline$ Quotient Property: $\log_b(P) - \log_b(Q) = \log_b\left(\frac{P}{Q}\right)$ $\newline$ So, $\log_{6}(u^2) - \log_{6}(v^8) = \log_{6}\left(\frac{u^2}{v^8}\right)$
Write Final Answer: Write the final answer as a single logarithm. $\newline$ The expression is now condensed to a single logarithm: $\newline$ $\log_{6}\left(\frac{u^2}{v^8}\right)$