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Convert the exponential equation in logarithmic form.\newline15−1=11515^{-1} = \frac{1}{15}

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Full solution

Q. Convert the exponential equation in logarithmic form.\newline15−1=11515^{-1} = \frac{1}{15}
  1. Identify variables: Identify bb, xx, and yy. Compare 15−1=11515^{-1} = \frac{1}{15} with by=xb^y = x. b=15b = 15 x=115x = \frac{1}{15} y=−1y = -1
  2. Convert to logarithmic form: Convert the exponential equation to logarithmic form. Substitute b=15b=15, x=115x=\frac{1}{15}, and y=−1y=-1 in log⁡b(x)=y\log_b(x) = y. Logarithmic equation: log⁡15(115)=−1\log_{15}\left(\frac{1}{15}\right) = -1
  3. Verify the solution: Check the final answer. Exponential equation: 15−1=11515^{-1} = \frac{1}{15} Logarithmic equation: log⁡15(115)=−1\log_{15}\left(\frac{1}{15}\right) = -1

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