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Solve the following logarithm problem for the positive solution for x. log_(6)x=-3 Answer:

Solve the following logarithm problem for the positive solution for x x .\newlinelog⁡6x=−3 \log _{6} x=-3 \newlineAnswer:

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Full solution

Q. Solve the following logarithm problem for the positive solution for x x .\newlinelog⁡6x=−3 \log _{6} x=-3 \newlineAnswer:
  1. Convert to Exponential Form: Convert the logarithmic equation to its equivalent exponential form.\newlineThe logarithmic equation log⁡6x=−3\log_{6} x = -3 can be rewritten in exponential form as 66 raised to the power of −3-3 equals xx.\newlineCalculation: 6−3=x6^{-3} = x
  2. Calculate Value: Calculate the value of 66 raised to the power of −3-3.\newlineTo find the value of 6−36^{-3}, we take the reciprocal of 66 cubed.\newlineCalculation: 6−3=163=16×6×6=12166^{-3} = \frac{1}{6^3} = \frac{1}{6\times6\times6} = \frac{1}{216}
  3. Verify Positivity: Verify that the solution is positive.\newlineThe value we found for xx is 1216\frac{1}{216}, which is a positive number.

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