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Rewrite the following in the form log(c). 2log(4)

Rewrite the following in the form log⁡(c) \log (c) .\newline2log⁡(4) 2 \log (4)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newline2log⁡(4) 2 \log (4)
  1. Identify Property: Identify the logarithmic property to simplify 2log⁡(4)2\log(4). The power property of logarithms states that a coefficient can be turned into an exponent inside the logarithm. So, 2log⁡(4)2\log(4) can be rewritten as log⁡(42)\log(4^2).
  2. Calculate Value: Calculate the value of 424^2 and rewrite the logarithm.\newline424^2 equals 1616, so log⁡(42)\log(4^2) becomes log⁡(16)\log(16).
  3. Verify Expression Form: Verify that the final expression is in the form log⁡(c)\log(c). The expression log⁡(16)\log(16) is indeed in the form log⁡(c)\log(c), where cc is a constant.

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