Consider the equation 4*e^(2.7 x)=33". " 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 e^(2.7x) by dividing both sides of the equation by 4. Calculation: 4*e^(2.7x) = 33 => e^(2.7x) = 33/4Take natural logarithm: Take the natural logarithm (log base e, denoted as ln) of both sides to solve for x. Calculation: ln(e^(2.7x)) = ln(33/4)Apply logarithm property: Apply the property of logarithms that ln(e^y) = y to simplify the left side of the equation. Calculation: 2.7x = ln(33/4)Solve for x: Solve for x by dividing both sides of the equation by 2.7. Calculation: x = ln(33/4) / 2.7Approximate x value: Approximate the value of x using a calculator. Calculation: x ≈ ln(33/4) / 2.7 ≈ ln(8.25) / 2.7 ≈ 2.1102 / 2.7 ≈ 0.781

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Consider the equation

4*e^(2.7 x)=33". "
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 $\newline$ $4 \cdot e^{2.7 x}=33 \text {. }$ $\newline$ Solve the equation for $x$ . Express the solution as a logarithm in base $e$ . $\newline$ $x=$ $\newline$ Approximate the value of $x$ . Round your answer to the nearest thousandth. $\newline$ $x \approx$

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Math Problems

Algebra 2

Change of base formula

Full solution

Q. Consider the equation

\newline

4 \cdot e^{2.7 x}=33 \text {. }

\newline

Solve the equation for

x

. Express the solution as a logarithm in base

e

\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 $e^{2.7x}$ by dividing both sides of the equation by $4$ . $\newline$ Calculation: $4\cdot e^{2.7x} = 33 \Rightarrow e^{2.7x} = \frac{33}{4}$
Take natural logarithm: Take the natural logarithm (log base $e$ , denoted as $\ln$ ) of both sides to solve for $x$ . $\newline$ Calculation: $\ln(e^{2.7x}) = \ln(\frac{33}{4})$
Apply logarithm property: Apply the property of logarithms that $\ln(e^y) = y$ to simplify the left side of the equation. $\newline$ Calculation: $2.7x = \ln(\frac{33}{4})$
Solve for x: Solve for x by dividing both sides of the equation by $2.7$ . $\newline$ Calculation: $x = \frac{\ln(\frac{33}{4})}{2.7}$
Approximate x value: Approximate the value of x using a calculator. $\newline$ Calculation: $x \approx \ln(\frac{33}{4}) / 2.7 \approx \ln(8.25) / 2.7 \approx 2.1102 / 2.7 \approx 0.781$