Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR.
-Given that $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$, find $\log _{10} \frac{27}{4}$
A) 0.0512
B) 0.8293
C) 0.2549
D) 1.8572

Question

Quizplus · Accepted Answer

The given expression can be simplified using the properties of logarithms: $\log _{10} \frac{27}{4} = \log _{10} 27 - \log _{10} 4$. Since $27 = 3^3$ and $4 = 2^2$, this becomes $3\log _{10} 3 - 2\log _{10} 2$. Substituting the given values, we get $3(0.4771) - 2(0.3010) = 1.4313 - 0.6020 = 0.8293$.

Evaluate the Given Logarithm by Applying the Appropriate Rule(s) log⁡102=0.3010\log _{10} 2=0.3010log10​2=0.3010

Evaluate the Given Logarithm by Applying the Appropriate Rule(s) $\log _{10} 2=0.3010$