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Consider the equation -16*10^(6x)=-80". " Solve the equation for x. Express the solution as a logarithm in base10. x= Approximate the value of x. Round your answer to the nearest thousandth. x~~

Consider the equation\newline−16⋅106x=−80.  -16 \cdot 10^{6 x}=-80 \text {. } \newlineSolve the equation for x x . Express the solution as a logarithm in base1010.\newlinex= x= \newlineApproximate the value of x x . Round your answer to the nearest thousandth.\newlinex≈ x \approx

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Q. Consider the equation\newline−16⋅106x=−80.  -16 \cdot 10^{6 x}=-80 \text {. } \newlineSolve the equation for x x . Express the solution as a logarithm in base1010.\newlinex= x= \newlineApproximate the value of x x . Round your answer to the nearest thousandth.\newlinex≈ x \approx
  1. Isolate exponential term: First, let's isolate the exponential term by dividing both sides by -16＂).\(\newline\$-16\cdot10^{(6x)} = -80\)\(\newline\)\(10^{(6x)} = \frac{-80}{-16}\)\(\newline\)\(10^{(6x)} = 5\)
  2. Take logarithm: Now, we'll take the logarithm of both sides to solve for \(6x\).\[\log(10^{6x}) = \log(5)\]\[6x = \log(5)\]
  3. Divide by \(6\): Next, we divide both sides by \(6\) to solve for \(x\).\[x = \frac{\log(5)}{6}\]
  4. Calculate approximate value: Finally, we'll use a calculator to approximate the value of \(x\).\(\newline\)\(x \approx \log(5) / 6\)\(\newline\)\(x \approx 0.1139\) (rounded to the nearest thousandth)

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