Write the following as a single logarithm. Assume all variables are positive. $$ 4 \log _{4}(z)+4 \log _{4}(a)=\square $$ Preview

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$$ 4 \log _{4}(z \cdot a) $$ To write the given expression as a single logarithm, we can use the properties of logarithms. Specifically, we'll use the product rule, which states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. The given expression is: $$ 4 \log _{4}(z) + 4 \log _{4}(a) $$ First, we can factor out the common factor of 4 from both terms: $$ 4(\log _{4}(z) + \log _{4}(a)) $$ Now, we can apply the product rule of logarithms, which states that: $$ \log_b(x) + \log_b(y) = \log_b(xy) $$ Using this rule, we can combine the two logarithms inside the parentheses: $$ 4 \log _{4}(z \cdot a) $$ So, the expression $$ 4 \log _{4}(z) + 4 \log _{4}(a) $$ can be written as a single logarithm as: $$ 4 \log _{4}(z \cdot a) $$

Write the following as a single logarithm. Assume all variables are positive. \( 4 \log _{4}(z)+4 \log _{4}(a)=\square \) Preview

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Write the following as a single logarithm. Assume all variables are positive. \( 4 \log _{4}(z)+4 \log _{4}(a)=\square \) Preview

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