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Write the log equation as an exponential equation. You do not need to solve for x. log_(4x)(2x-7)=3x-5 Answer:

Write the log equation as an exponential equation. You do not need to solve for x \mathrm{x} .\newlinelog⁡4x(2x−7)=3x−5 \log _{4 x}(2 x-7)=3 x-5 \newlineAnswer:

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Full solution

Q. Write the log equation as an exponential equation. You do not need to solve for x \mathrm{x} .\newlinelog⁡4x(2x−7)=3x−5 \log _{4 x}(2 x-7)=3 x-5 \newlineAnswer:
  1. Rewrite as Exponential Equation: The logarithmic equation log⁡4x(2x−7)=3x−5\log_{4x}(2x-7)=3x-5 can be rewritten as an exponential equation by using the definition of a logarithm. The definition states that if log⁡a(b)=c\log_{a}(b)=c, then ac=ba^{c}=b. Here, aa is the base of the logarithm, bb is the argument, and cc is the logarithm's value.
  2. Use Logarithm Definition: Using the definition, we can rewrite log⁡4x(2x−7)=3x−5\log_{4x}(2x-7)=3x-5 as (4x)3x−5=2x−7(4x)^{3x-5}=2x-7. This is because the base is 4x4x, the argument is 2x−72x-7, and the value of the logarithm is 3x−53x-5.

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