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

Write the log equation as an exponential equation. You do not need to solve for x \mathrm{x} .\newlinelog⁡(x+4)(5x)=x \log _{(x+4)}(5 x)=x \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⁡(x+4)(5x)=x \log _{(x+4)}(5 x)=x \newlineAnswer:
  1. Apply Definition of Logarithm: We have the logarithmic equation: log⁡(x+4)(5x)=x\log_{(x+4)}(5x) = x. To convert this to an exponential equation, we use the definition of a logarithm. The definition states that if log⁡(b)(a)=c\log_{(b)}(a) = c, then bc=ab^c = a.
  2. Convert to Exponential Equation: Using the definition, we can rewrite the given logarithmic equation as an exponential equation. The base of the logarithm becomes the base of the exponent, the right side of the logarithmic equation becomes the exponent, and the number inside the logarithm becomes the result of the exponentiation. Therefore, (x+4)x=5x (x+4)^x = 5x .

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