Evaluate: 4 log 4 + 3 log 5 - log 2.

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I will solve question 7. Question 7: Evaluate: 2log 4 + 3log 5 − log 2. (Note: The question appears to have a handwritten correction from 4log 4² to 2log 4. I will proceed with the corrected version 2log 4 + 3log 5 − log 2, assuming the base of the logarithm is 10.) Step 1: Apply the power rule of logarithms, which states that a log b = log b^a. 2log 4 = log 4² = log 16; 3log 5 = log 5³ = log 125 Step 2: Substitute these back into the original expression. The expression becomes: log 16 + log 125 − log 2 Step 3: Apply the product rule of logarithms, which states that log a + log b = log (a × b). log 16 + log 125 = log (16 × 125); log (16 × 125) = log 2000; Step 4: Apply the quotient rule of logarithms, which states that log a − log b = log (a/b). log 2000 − log 2 = log (2000/2); log (2000/2) = log 1000 Step 5: Evaluate log 1000. Since the base of the logarithm is 10 (when not specified), we are looking for the power to which 10 must be raised to get 1000. 10³ = 1000; Therefore, log 1000 = 3. The final answer is 3. The correct option is A. A. 3

Evaluate: 4 log 4 + 3 log 5 - log 2.

Answer

Step-by-step solution

Apply the power rule of logarithms, which states that $a \log b = \log b^a$ .

Substitute these back into the original expression.

Apply the product rule of logarithms, which states that $\log a + \log b = \log (a \times b)$ .

Apply the quotient rule of logarithms, which states that $\log a - \log b = \log \left(\frac{a}{b}\right)$ .

Evaluate $\log 1000$ .

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Evaluate: 4 log 4 + 3 log 5 - log 2.

Answer

Step-by-step solution

Apply the power rule of logarithms, which states that alog⁡b=log⁡baa \log b = \log b^aalogb=logba.

Substitute these back into the original expression.

Apply the product rule of logarithms, which states that log⁡a+log⁡b=log⁡(a×b)\log a + \log b = \log (a \times b)loga+logb=log(a×b).

Apply the quotient rule of logarithms, which states that log⁡a−log⁡b=log⁡(ab)\log a - \log b = \log \left(\frac{a}{b}\right)loga−logb=log(ba​).

Evaluate log⁡1000\log 1000log1000.

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More Mathematics Questions

Apply the power rule of logarithms, which states that $a \log b = \log b^a$ .

Apply the product rule of logarithms, which states that $\log a + \log b = \log (a \times b)$ .

Apply the quotient rule of logarithms, which states that $\log a - \log b = \log \left(\frac{a}{b}\right)$ .

Evaluate $\log 1000$ .