Consider the equation 5*e^(-7x)=12". " Solve the equation for x. Express the solution as a logarithm in base e. x= Approximate the value of x. Round your answer to the nearest thousandth. x~~

Isolate exponential term: Isolate the exponential term. To solve for x, we first need to isolate the exponential term e^(-7x) by dividing both sides of the equation by 5. 5 * e^(-7x) = 12 e^(-7x) = 12 / 5 e^(-7x) = 2.4Take natural logarithm: Take the natural logarithm of both sides. To solve for the exponent, we take the natural logarithm (log base e, also known as ln) of both sides of the equation. ln(e^(-7x)) = ln(2.4)Apply logarithmic property: Apply the logarithmic property. Using the property that ln(e^y) = y, we can simplify the left side of the equation. -7x = ln(2.4)Solve for x: Solve for x. Now, we divide both sides by -7 to solve for x. x = ln(2.4) / -7Approximate x value: Approximate the value of x. Using a calculator, we can find the approximate value of x. x ≈ ln(2.4) / -7 x ≈ -0.087/ -7 x ≈ 0.0124 Rounded to the nearest thousandth, x ≈ 0.012.

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Consider the equation

5*e^(-7x)=12". "
Solve the equation for
x. Express the solution as a logarithm in base
e.

x=
Approximate the value of
x. Round your answer to the nearest thousandth.

x~~

Consider the equation $\newline$ $5 \cdot e^{-7 x}=12 \text {. }$ $\newline$ Solve the equation for $x$ . Express the solution as a logarithm in basee. $\newline$ $x=$ $\newline$ Approximate the value of $x$ . Round your answer to the nearest thousandth. $\newline$ $x \approx$

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Algebra 2

Change of base formula

Full solution

Q. Consider the equation

\newline

5 \cdot e^{-7 x}=12 \text {. }

\newline

Solve the equation for

x

. Express the solution as a logarithm in basee.

\newline

x=

\newline

Approximate the value of

x

. Round your answer to the nearest thousandth.

\newline

x \approx

Isolate exponential term: Isolate the exponential term. $\newline$ To solve for $x$ , we first need to isolate the exponential term $e^{(-7x)}$ by dividing both sides of the equation by $5$ . $\newline$ $5 \cdot e^{(-7x)} = 12$ $\newline$ $e^{(-7x)} = \frac{12}{5}$ $\newline$ $e^{(-7x)} = 2.4$
Take natural logarithm: Take the natural logarithm of both sides. $\newline$ To solve for the exponent, we take the natural logarithm (log base $e$ , also known as $\ln$ ) of both sides of the equation. $\newline$ $\ln(e^{-7x}) = \ln(2.4)$
Apply logarithmic property: Apply the logarithmic property. $\newline$ Using the property that $\ln(e^y) = y$ , we can simplify the left side of the equation. $\newline$ $-7x = \ln(2.4)$
Solve for x: Solve for x. $\newline$ Now, we divide both sides by $-7$ to solve for x. $\newline$ $x = \frac{\ln(2.4)}{-7}$
Approximate x value: Approximate the value of $x$ . Using a calculator, we can find the approximate value of $x$ . $x \approx \frac{\ln(2.4)}{-7}$ $x \approx \frac{-0.087}{-7}$ $x \approx 0.0124$ Rounded to the nearest thousandth, $x \approx 0.012$ .