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-15*2^(-0.5 x)=-90 What is the solution of the equation? Round your answer, if necessary, to the nearest thousandth. x~~

−15⋅2−0.5x=−90 -15 \cdot 2^{-0.5 x}=-90 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinex≈ x \approx

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Q. −15⋅2−0.5x=−90 -15 \cdot 2^{-0.5 x}=-90 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinex≈ x \approx
  1. Write equation: Write down the given equation.\newlineWe have the equation −15⋅2(−0.5x)=−90-15 \cdot 2^{(-0.5 x)} = -90.
  2. Divide by ext{-}1515: Divide both sides of the equation by ext{-}1515 to isolate the exponential term.\newline ext{-}9090 / ext{-}1515 = 22^{( ext{-}00.55 x)} / ext{-}1515\newline6=2(ext−0.5x)6 = 2^{( ext{-}0.5 x)}
  3. Apply logarithm: Apply the logarithm to both sides of the equation to solve for x.\newlinelog⁡(6)=log⁡(2−0.5x)\log(6) = \log(2^{-0.5 x})\newlineUse the power property of logarithms to bring down the exponent.\newlinelog⁡(6)=−0.5x⋅log⁡(2)\log(6) = -0.5 x \cdot \log(2)
  4. Isolate x: Isolate x by dividing both sides by −0.5log⁡(2)-0.5 \log(2).\newlinex=log⁡(6)(−0.5⋅log⁡(2))x = \frac{\log(6)}{(-0.5 \cdot \log(2))}
  5. Calculate x: Calculate the value of x using a calculator.\newlinex=log⁡(6)−0.5×log⁡(2)x = \frac{\log(6)}{-0.5 \times \log(2)}\newlinex≈5.169925001−0.5×0.3010299957x \approx \frac{5.169925001}{-0.5 \times 0.3010299957}\newlinex≈5.169925001−0.15051499785x \approx \frac{5.169925001}{-0.15051499785}\newlinex≈−34.343x \approx -34.343

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