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

Rewrite the following in the form log⁡(c) \log (c) .\newline2log⁡(5) 2 \log (5)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newline2log⁡(5) 2 \log (5)
  1. Given expression: We are given the expression 2log⁡(5)2\log(5). To rewrite this expression in the form log⁡(c)\log(c), we can use the power property of logarithms, which states that n⋅log⁡b(a)=log⁡b(an)n \cdot \log_b(a) = \log_b(a^n). We will apply this property to the given expression.
  2. Applying power property: Using the power property, we rewrite 2log⁡(5)2\log(5) as log⁡(52)\log(5^2).\newlineCalculation: 2log⁡(5)=log⁡(52)2\log(5) = \log(5^2)
  3. Calculating value of c: Now we calculate 525^2 to find the value of cc.\newlineCalculation: 52=255^2 = 25
  4. Substituting value in expression: We substitute 2525 for 525^2 in the logarithmic expression.log⁡(52)\log(5^2) becomes log⁡(25)\log(25).

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