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Rewrite the following in the form log(c). 3log(4)

Rewrite the following in the form log⁡(c) \log (c) .\newline3log⁡(4) 3 \log (4)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newline3log⁡(4) 3 \log (4)
  1. Recognize Property: Recognize the logarithmic property to be used.\newlineThe expression 3log⁡(4)3\log(4) involves a constant multiple of a logarithm. According to the power rule of logarithms, a constant multiple of a logarithm can be rewritten as the logarithm of a number raised to a power.
  2. Apply Rule: Apply the power rule of logarithms.\newlineThe power rule states that a constant multiple of a logarithm is equivalent to the logarithm of the base raised to the power of that constant. Therefore, 3log⁡(4)3\log(4) can be rewritten as log⁡(43)\log(4^3).
  3. Calculate Value: Calculate the value of 434^3. \newline43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  4. Write Final Expression: Write the final expression using the result from Step 33.\newlineThe expression 3log⁡(4)3\log(4) is equivalent to log⁡(64)\log(64).

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