Question

use properties of logarithms to condense the logarithmic expression below. write the expression as a single logarithm whose coefficient is 1. where possible, evaluate logarithmic expressions. \\(\log y + 10 \log z = \square\\) \\(5\\) of \\(25\\) this test: \\(25\\) point(s) possible this question: \\(1\\) point(s) possible

Explanation:

Step1: Apply Power Rule

The power rule of logarithms states that \( n\log_b M=\log_b M^n \). For \( 10\log z \), we can rewrite it as \( \log z^{10} \).

Step2: Apply Product Rule

The product rule of logarithms states that \( \log_b M+\log_b N = \log_b(MN) \). Now we have \( \log y+\log z^{10} \), applying the product rule gives \( \log(y\times z^{10})=\log(yz^{10}) \).

Answer:

\(\log(yz^{10})\)