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Express the given expression as an integer or as a fraction in simplest form. (7^(log_(7)6)) Answer:

Express the given expression as an integer or as a fraction in simplest form.\newline(7log⁡76) \left(7^{\log _{7} 6}\right) \newlineAnswer:

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Full solution

Q. Express the given expression as an integer or as a fraction in simplest form.\newline(7log⁡76) \left(7^{\log _{7} 6}\right) \newlineAnswer:
  1. Recognize Property of Logarithms: Recognize the property of logarithms that states alog⁡a(b)=ba^{\log_a(b)} = b. Here, we have 7log⁡7(6)7^{\log_{7}(6)}, which means we can apply this property.
  2. Apply Property to Simplify: Apply the property to simplify the expression.\newlineSince the base of the logarithm 77 matches the base of the exponent 77, we can simplify the expression to just the argument of the logarithm, which is 66.\newlineSo, 7log⁡76=67^{\log_{7}6} = 6.

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