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Rewrite the following in the form log(c). 5log(2)

Rewrite the following in the form log⁡(c) \log (c) .\newline5log⁡(2) 5 \log (2)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newline5log⁡(2) 5 \log (2)
  1. Identify Property: Identify the property of logarithms to simplify 5log⁡(2)5\log(2). The power property of logarithms states that a constant multiple of a logarithm can be written as the logarithm of the base raised to the power of that constant. 5log⁡(2)5\log(2) can be rewritten as log⁡(25)\log(2^5).
  2. Calculate Value: Calculate the value of 252^5. \newline25=2×2×2×2×2=322^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32. \newlineSo, log⁡(25)\log(2^5) is equivalent to log⁡(32)\log(32).
  3. Write Final Answer: Write the final answer.\newlineThe expression 5log⁡(2)5\log(2) has been rewritten as log⁡(32)\log(32).

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