Use properties of logarithms to evaluate the expression.

Ask by Bartlett Nguyen. in the United States

Jan 24,2025

Question

Use properties of logarithms to evaluate the expression. $$ 2 \log 5+\log 4 $$ $$ \square $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ 2 \log(5)+\log(4) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2\log_{10}{\left(5ight)}+\log_{10}{\left(4ight)}$$
- step1: Rewrite the expression:
  $$\log_{10}{\left(5^{2}ight)}+\log_{10}{\left(4ight)}$$
- step2: Use the logarithm product rule:
  $$\log_{10}{\left(5^{2}	imes 4ight)}$$
- step3: Multiply the numbers:
  $$\log_{10}{\left(100ight)}$$
- step4: Write in exponential form:
  $$\log_{10}{\left(10^{2}ight)}$$
- step5: Simplify the expression:
  $$2$$
The expression $$2 \log 5 + \log 4$$ simplifies to $$2$$.
The expression simplifies to 2.

Use properties of logarithms to evaluate the expression.

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