Consider the equation -3*e^(5w)=-88". " Solve the equation for w. Express the solution as a logarithm in base e. w= Approximate the value of w. Round your answer to the nearest thousandth. w~~

Question

Consider the equation  -3*e^(5w)=-88". " Solve the equation for  w. Express the solution as a logarithm in base e.  w= Approximate the value of  w. Round your answer to the nearest thousandth.  w~~

Bytelearn · Accepted Answer

Isolate exponential term: Isolate the exponential term. To solve for w, we first need to isolate the exponential term e^(5w). We do this by dividing both sides of the equation by -3. Calculation: -3*e^(5w) = -88 | :(-3) e^(5w) = 88/3Take natural logarithm: Take the natural logarithm of both sides. To solve for the exponent, we take the natural logarithm (ln) of both sides of the equation, because ln and the exponential function are inverse operations. Calculation: ln(e^(5w)) = ln(88/3)Apply property of logarithms: Apply the property of logarithms. Using the property of logarithms that ln(e^x) = x, we can simplify the left side of the equation. Calculation: 5w = ln(88/3)Solve for w: Solve for w. Now, we divide both sides of the equation by 5 to solve for w. Calculation: w = ln(88/3) / 5Approximate value of w: Approximate the value of w. Using a calculator, we can find the numerical value of w. Calculation: w ≈ ln(88/3) / 5 w ≈ ln(29.3333...) / 5 w ≈ 3.3771 / 5 w ≈ 0.67542 Rounded to the nearest thousandth: w ≈ 0.675

Consider the equation $\newline$ $-3 \cdot e^{5 w}=-88 \text {. }$ $\newline$ Solve the equation for $w$ . Express the solution as a logarithm in basee. $\newline$ $w=$ $\newline$ Approximate the value of $w$ . Round your answer to the nearest thousandth. $\newline$ $w \approx$

Full solution

More problems from Solve polynomial equations

Related topics