Express the given expression as an integer or as a fraction in simplest form. log_(3)((1)/(root(4)(3^(5)))) Answer:

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Express the given expression as an integer or as a fraction in simplest form.  log_(3)((1)/(root(4)(3^(5)))) Answer:

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Understand the expression: Understand the given expression. We need to simplify the expression log_(3)((1)/(root(4)(3^(5)))). This means we are looking for the exponent that 3 must be raised to, to get the value (1)/(root(4)(3^(5))).Simplify fraction denominator: Simplify the denominator of the fraction inside the logarithm. The denominator is the fourth root of 3^5, which can be written as (3^5)^(1/4).Apply power rule of exponents: Apply the power rule of exponents to the denominator. When raising a power to another power, we multiply the exponents. So, (3^5)^(1/4) becomes 3^(5/4).Rewrite using properties of logarithms: Rewrite the expression using the properties of logarithms. The expression log_(3)((1)/(3^(5/4))) can be rewritten using the quotient rule of logarithms as log_(3)(1) - log_(3)(3^(5/4)).Simplify the logarithms: Simplify the logarithms. We know that log_(3)(1) is 0 because any number raised to the power of 0 is 1. Also, log_(3)(3^(5/4)) is simply 5/4 because the base of the logarithm and the base of the exponent are the same. So, the expression becomes 0 - 5/4.Subtract to find answer: Subtract the values to find the final answer. 0 - 5/4 is simply -5/4.

Express the given expression as an integer or as a fraction in simplest form. $\newline$ $\log _{3}\left(\frac{1}{\sqrt[4]{3^{5}}}\right)$ $\newline$ Answer:

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Express the given expression as an integer or as a fraction in simplest form. $\newline$ $\log _{3}\left(\frac{1}{\sqrt[4]{3^{5}}}\right)$ $\newline$ Answer: