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Solve the following logarithm problem for the positive solution for x. log_(125)x=-(4)/(3) Answer:

Solve the following logarithm problem for the positive solution for x x .\newlinelog⁡125x=−43 \log _{125} x=-\frac{4}{3} \newlineAnswer:

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Quotient property of logarithmsright chevron icon

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Q. Solve the following logarithm problem for the positive solution for x x .\newlinelog⁡125x=−43 \log _{125} x=-\frac{4}{3} \newlineAnswer:
  1. Understand the logarithmic equation: Understand the logarithmic equation.\newlineThe given logarithmic equation is log⁡125x=−43\log_{125}x = -\frac{4}{3}. This means that 125125 raised to the power of −43-\frac{4}{3} equals xx.
  2. Convert to exponential form: Convert the logarithmic form to exponential form.\newlineUsing the definition of a logarithm, we can rewrite the equation in exponential form: 125−(4/3)=x125^{-(4/3)} = x.
  3. Simplify the exponential expression: Simplify the exponential expression.\newlineSince 125125 is 535^3, we can rewrite the equation as (53)−(4/3)=x(5^3)^{-(4/3)} = x. Simplifying the exponent, we get 5−4=x5^{-4} = x.
  4. Calculate x: Calculate the value of x.\newline5−45^{-4} means 154\frac{1}{5^4}. Therefore, x=154=1625x = \frac{1}{5^4} = \frac{1}{625}.

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