Evaluate 4*e^(2.7x)=33

$4 \cdot e^{2.7 x} = 33$

Step 1

Divide each term in $(4 \cdot e^{2.7 x}) = 33$ by $4$ and simplify.

Divide each term in $(4 \cdot e^{2.7 x}) = 33$ by $4$ .

$\frac{(4 \cdot e^{2.7 x})}{4} = \frac{33}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \cdot e^{2.7 x}}{4} = \frac{33}{4}$

Divide $e^{2.7 x}$ by $1$ .

$e^{2.7 x} = \frac{33}{4}$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{2.7 x}) = \ln (\frac{33}{4})$

Step 3

Expand the left side.

Expand $\ln (e^{2.7 x})$ by moving $2.7 x$ outside the logarithm.

$2.7 x \ln (e) = \ln (\frac{33}{4})$

The natural logarithm of $e$ is $1$ .

$2.7 x \cdot 1 = \ln (\frac{33}{4})$

Multiply $2.7$ by $1$ .

$2.7 x = \ln (\frac{33}{4})$

Step 4

Divide each term in $2.7 x = \ln (\frac{33}{4})$ by $2.7$ and simplify.

Divide each term in $2.7 x = \ln (\frac{33}{4})$ by $2.7$ .

$\frac{2.7 x}{2.7} = \frac{\ln (\frac{33}{4})}{2.7}$

Simplify the left side.

Cancel the common factor of $2.7$ .

Cancel the common factor.

$\frac{2.7 x}{2.7} = \frac{\ln (\frac{33}{4})}{2.7}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{33}{4})}{2.7}$

Simplify the right side.

Replace $e$ with an approximation.

$x = \frac{\log_{2.71828182} (\frac{33}{4})}{2.7}$

Divide $33$ by $4$ .

$x = \frac{\log_{2.71828182} (8.25)}{2.7}$

Log base $2.71828182$ of $8.25$ is approximately $2.1102132$ .

$x = \frac{2.1102132}{2.7}$

Divide $2.1102132$ by $2.7$ .

$x = 0.78156044$