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Write the log equation as an exponential equation. log_(5x)(x+1)=(8)/(3) Answer Aftempt 2 out of 2 5x^((8)/(3))=x+1

\newlineWrite the log equation as an exponential equation. \newlinelog⁡5x(x+1)=83 \log _{5 x}(x+1)=\frac{8}{3}

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Q. \newlineWrite the log equation as an exponential equation. \newlinelog⁡5x(x+1)=83 \log _{5 x}(x+1)=\frac{8}{3}
  1. Understand Logarithmic Equation: Understand the logarithmic equation and convert it to exponential form. log⁡5x(x+1)=83\log_{5x}(x+1) = \frac{8}{3} can be rewritten as 5x(83)=x+15x^{\left(\frac{8}{3}\right)} = x + 1.
  2. Convert to Exponential Form: Check if the conversion from logarithmic to exponential form is correct.\newlineFrom log⁡b(a)=c\log_b(a) = c, we get bc=ab^c = a. Here, b=5xb = 5x, a=x+1a = x + 1, and c=83c = \frac{8}{3}. So, 5x83=x+15x^{\frac{8}{3}} = x + 1 is correct.

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