Understand Logarithm Properties: Understand the properties of logarithms. We can use the quotient rule for logarithms, which states that log_b(M) - log_b(N) = log_b(M/N), where b is the base of the logarithms.Apply Quotient Rule: Apply the quotient rule to the given expression. log_(8)63 - log_(8)9 becomes log_(8)(63/9).Simplify Fraction: Simplify the fraction inside the logarithm. 63/9 simplifies to 7. So, log_(8)63 - log_(8)9 becomes log_(8)7.Evaluate Logarithm: Evaluate log_(8)7. Since 7 cannot be expressed as a power of 8, the logarithm does not simplify to a nice whole number or fraction. The value of log_(8)7 is not an integer or a simple fraction, and it is typically left as is or approximated using a calculator.

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$\log_{8}63-\log_{8}9=$

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\log_{8}63-\log_{8}9=

Understand Logarithm Properties: Understand the properties of logarithms. We can use the quotient rule for logarithms, which states that $\log_b(M) - \log_b(N) = \log_b\left(\frac{M}{N}\right)$ , where $b$ is the base of the logarithms.
Apply Quotient Rule: Apply the quotient rule to the given expression. $\log_{8}63 - \log_{8}9$ becomes $\log_{8}(\frac{63}{9})$ .
Simplify Fraction: Simplify the fraction inside the logarithm. $\newline$ $\frac{63}{9}$ simplifies to $7$ . $\newline$ So, $\log_{8}63 - \log_{8}9$ becomes $\log_{8}7$ .
Evaluate Logarithm: Evaluate $\log_{8}7$ . Since $7$ cannot be expressed as a power of $8$ , the logarithm does not simplify to a nice whole number or fraction. The value of $\log_{8}7$ is not an integer or a simple fraction, and it is typically left as is or approximated using a calculator.