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Consider the equation -16*10^(6x)=-80". " Solve the equation for x. Express the solution as a logarithm in base-10. x= Approximate the value of x. Round your answer to the nearest thousandth. x~~

Consider the equation\newline−16×106x=−80-16 \times 10^{6x} = -80. \newlineSolve the equation for \newlinexx. Express the solution as a logarithm in base−10-10.\newlinex=x=\newlineApproximate the value of \newlinexx. Round your answer to the nearest thousandth.\newlinex≈x \approx

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Q. Consider the equation\newline−16×106x=−80-16 \times 10^{6x} = -80. \newlineSolve the equation for \newlinexx. Express the solution as a logarithm in base−10-10.\newlinex=x=\newlineApproximate the value of \newlinexx. Round your answer to the nearest thousandth.\newlinex≈x \approx
  1. Identify Equation: Identify the equation that needs to be solved.\newlineThe equation given is −16×106x=−80-16\times10^{6x} = -80.
  2. Isolate Exponential Term: Isolate the exponential term.\newlineTo isolate the exponential term, divide both sides of the equation by \(-16＂).\newline\(-16\cdot1010^{(66x)} / −16-16 = −80-80 / −16-16＂)\newline\(10^{(66x)} = 55＂)
  3. Apply Logarithm: Apply the logarithm to both sides of the equation.\newlineTo solve for xx, take the logarithm of both sides of the equation. We will use the base-1010 logarithm since the exponential base is 1010.\newlinelog⁡(106x)=log⁡(5)\log(10^{6x}) = \log(5)
  4. Use Power Property: Use the power property of logarithms.\newlineThe power property of logarithms states that log⁡b(mn)=n⋅log⁡b(m)\log_b(m^n) = n \cdot \log_b(m). Apply this property to the left side of the equation.\newline6x⋅log⁡(10)=log⁡(5)6x \cdot \log(10) = \log(5)
  5. Simplify Equation: Simplify the left side of the equation.\newlineSince log⁡(10)\log(10) is equal to 11, the equation simplifies to:\newline6x=log⁡(5)6x = \log(5)
  6. Solve for x: Solve for x.\newlineDivide both sides of the equation by 66 to solve for xx.\newlinex=log⁡(5)6x = \frac{\log(5)}{6}
  7. Approximate Value: Approximate the value of xx. Use a calculator to find the value of log⁡(5)\log(5) and then divide by 66. x≈log⁡(5)/6x \approx \log(5) / 6 x≈0.69897/6x \approx 0.69897 / 6 x≈0.116495x \approx 0.116495 Round the answer to the nearest thousandth. x≈0.116x \approx 0.116

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