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Consider the equation

2*e^(-6w)=95". "
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~~

Consider the equation $\newline$ $2 \cdot e^{-6 w}=95 \text {. }$ $\newline$ 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. $\newline$ $w \approx$

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Change of base formula

Full solution

Q. Consider the equation

\newline

2 \cdot e^{-6 w}=95 \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

Isolate exponential term: Isolate the exponential term $e^{-6w}$ by dividing both sides of the equation by $2$ . $\newline$ $2e^{-6w} = 95$ $\newline$ $e^{-6w} = \frac{95}{2}$ $\newline$ $e^{-6w} = 47.5$
Take natural logarithm: Take the natural logarithm (base $e$ ) of both sides to solve for $-6w$ . $\newline$ $\ln(e^{-6w}) = \ln(47.5)$ $\newline$ $-6w = \ln(47.5)$ because $\ln(e^x) = x$
Divide by $-6$ : Divide both sides by $-6$ to solve for $w$ . $\newline$ $w = \frac{\ln(47.5)}{-6}$
Approximate value: Approximate the value of $w$ using a calculator. $w \approx \frac{\ln(47.5)}{-6}$ $w \approx -0.621$

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