Recognize Properties: Recognize the properties of logarithms that can be applied to simplify the expression. The properties of logarithms that are relevant here are: - The Power Rule: log_b(a^c) = c*log_b(a) Using this property, we can take the coefficients in front of the logarithms and turn them into exponents inside the logarithms.Apply Power Rule: Apply the Power Rule to the given expression. We have 2log_(6)u - 8log_(6)v, which can be rewritten using the Power Rule as: log_(6)(u^2) - log_(6)(v^8)Combine Using Quotient Rule: Combine the two logarithms into a single logarithm using the Quotient Rule. The Quotient Rule for logarithms states that log_b(a) - log_b(c) = log_b(a/c). Applying this rule to our expression gives us: log_(6)(u^2/v^8)Check for Simplifications: Check for any possible simplifications of the expression inside the logarithm. In this case, there are no further simplifications that can be made to the expression u^2/v^8.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$1$ ) $2 \log _{6} u-8 \log _{6} v$

View step-by-step help

Home

Math Problems

Grade 8

Solve a system of equations using any method

Full solution

1

)

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

Recognize Properties: Recognize the properties of logarithms that can be applied to simplify the expression. $\newline$ The properties of logarithms that are relevant here are: $\newline$ - The Power Rule: $\log_b(a^c) = c\log_b(a)$ $\newline$ Using this property, we can take the coefficients in front of the logarithms and turn them into exponents inside the logarithms.
Apply Power Rule: Apply the Power Rule to the given expression. $\newline$ We have $2\log_{6}u - 8\log_{6}v$ , which can be rewritten using the Power Rule as: $\newline$ $\log_{6}(u^2) - \log_{6}(v^8)$
Combine Using Quotient Rule: Combine the two logarithms into a single logarithm using the Quotient Rule. $\newline$ The Quotient Rule for logarithms states that $\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)$ . $\newline$ Applying this rule to our expression gives us: $\newline$ $\log_{6}\left(\frac{u^2}{v^8}\right)$
Check for Simplifications: Check for any possible simplifications of the expression inside the logarithm. In this case, there are no further simplifications that can be made to the expression $u^2/v^8$ .