Simplify: log base 10 of 4 + log base 10 of 25

March 19, 2026Mathematics

ScanSolve AI Answer

March 19, 2026

Answer

Step 1: Apply the sum of logarithms property $\log_b m + \log_b n = \log_b (m n)$ .

\log_{10} 4 + \log_{10} 25 = \log_{10} (4 \cdot 25)

Step 2: Multiply the arguments.

4 \cdot 25 = 100

Substitute:

\log_{10} (4 \cdot 25) = \log_{10} 100

Step 3: Evaluate $\log_{10} 100$ .

Since $10^{2} = 100$ ,

\log_{10} 100 = 2

Final answer: 2

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Quick Answer

Apply the sum of logarithms property _b m + _b n = _b (m n). _10 4 + _10 25 = _10 (4 · 25) Step 2: Multiply the arguments.

Asked on March 19, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 19, 2026

Step 1: Apply the sum of logarithms property _b m + _b n = _b (m n). _10 4 + _10 25 = _10 (4 · 25) Step 2: Multiply the arguments. 4 · 25 = 100 Substitute: _10 (4 · 25) = _10 100 Step 3: Evaluate _10 100. Since 10^2 = 100, _10 100 = 2 Final answer: 2