Expand the Logarithmic Expression log base 4 of xy^6z^4

Problem

(log_4)(x*y6*z4)

Solution

1. Apply the product rule for logarithms, which states that (log_b)(M*N*P)=(log_b)(M)+(log_b)(N)+(log_b)(P)

(log_4)(x)+(log_4)(y6)+(log_4)(z4)

2. Apply the power rule for logarithms, which states that (log_b)(Mp)=p*(log_b)(M) to the terms with exponents.

(log_4)(x)+6*(log_4)(y)+4*(log_4)(z)

Final Answer

(log_4)(x*y6*z4)=(log_4)(x)+6*(log_4)(y)+4*(log_4)(z)

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