Simplify the logarithmic expression: 2 4 8

April 14, 2026Mathematics

ScanSolve AI Answer

April 14, 2026

Answer

Ngangwa, let's knock this out.

Step 1: Apply the power rule of logarithms, which states that $a \log_b x = \log_b x^a$ . $2 \log_4 8 = \log_4 (8^2)$

Step 2: Calculate $8^2$ . $8^2 = 64$ So the expression becomes: $\log_4 64$

Step 3: Evaluate $\log_4 64$ . This means finding the power to which 4 must be raised to get 64. Let $y = \log_4 64$ . This can be written in exponential form as $4^y = 64$ . We know that $4 \times 4 = 16$ , and $16 \times 4 = 64$ . So, $4^3 = 64$ . Therefore, $y = 3$ .

The value of the expression is: $\boxed{3}$ What's next?

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Quick Answer

Ngangwa, let's knock this out. Step 1: Apply the power rule of logarithms, which states that a _b x = _b x^a.

Asked on April 14, 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 April 14, 2026

Ngangwa, let's knock this out. Step 1: Apply the power rule of logarithms, which states that a _b x = _b x^a. 2 _4 8 = _4 (8^2) Step 2: Calculate 8^2. 8^2 = 64 So the expression becomes: _4 64 Step 3: Evaluate _4 64. This means finding the power to which 4 must be raised to get 64. Let y = _4 64. This can be written in exponential form as 4^y = 64. We know that 4 × 4 = 16, and 16 × 4 = 64. So, 4^3 = 64. Therefore, y = 3. The value of the expression is: 3 What's next?