Solve for x 6e^(0.25x+3)=26

$6 e^{0.25 x + 3} = 26$

Step 1

Divide each term in $6 e^{0.25 x + 3} = 26$ by $6$ and simplify.

Divide each term in $6 e^{0.25 x + 3} = 26$ by $6$ .

$\frac{6 e^{0.25 x + 3}}{6} = \frac{26}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 e^{0.25 x + 3}}{6} = \frac{26}{6}$

Divide $e^{0.25 x + 3}$ by $1$ .

$e^{0.25 x + 3} = \frac{26}{6}$

Simplify the right side.

Cancel the common factor of $26$ and $6$ .

Factor $2$ out of $26$ .

$e^{0.25 x + 3} = \frac{2 (13)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$e^{0.25 x + 3} = \frac{2 \cdot 13}{2 \cdot 3}$

Cancel the common factor.

$e^{0.25 x + 3} = \frac{2 \cdot 13}{2 \cdot 3}$

Rewrite the expression.

$e^{0.25 x + 3} = \frac{13}{3}$

Step 2

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

$\ln (e^{0.25 x + 3}) = \ln (\frac{13}{3})$

Step 3

Expand the left side.

Expand $\ln (e^{0.25 x + 3})$ by moving $0.25 x + 3$ outside the logarithm.

$(0.25 x + 3) \ln (e) = \ln (\frac{13}{3})$

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

$(0.25 x + 3) \cdot 1 = \ln (\frac{13}{3})$

Multiply $0.25 x + 3$ by $1$ .

$0.25 x + 3 = \ln (\frac{13}{3})$

Step 4

Subtract $3$ from both sides of the equation.

$0.25 x = \ln (\frac{13}{3}) - 3$

Step 5

Divide each term in $0.25 x = \ln (\frac{13}{3}) - 3$ by $0.25$ and simplify.

Divide each term in $0.25 x = \ln (\frac{13}{3}) - 3$ by $0.25$ .

$\frac{0.25 x}{0.25} = \frac{\ln (\frac{13}{3})}{0.25} + \frac{- 3}{0.25}$

Simplify the left side.

Cancel the common factor of $0.25$ .

Cancel the common factor.

$\frac{0.25 x}{0.25} = \frac{\ln (\frac{13}{3})}{0.25} + \frac{- 3}{0.25}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{13}{3})}{0.25} + \frac{- 3}{0.25}$

Simplify the right side.

Simplify each term.

Replace $e$ with an approximation.

$x = \frac{\log_{2.71828182} (\frac{13}{3})}{0.25} + \frac{- 3}{0.25}$

Divide $13$ by $3$ .

$x = \frac{\log_{2.71828182} (4.\overline{3})}{0.25} + \frac{- 3}{0.25}$

Log base $2.71828182$ of $4.\overline{3}$ is approximately $1.46633706$ .

$x = \frac{1.46633706}{0.25} + \frac{- 3}{0.25}$

Divide $1.46633706$ by $0.25$ .

$x = 5.86534827 + \frac{- 3}{0.25}$

Divide $- 3$ by $0.25$ .

$x = 5.86534827 - 12$

Subtract $12$ from $5.86534827$ .

$x = - 6.13465172$

Solve for x 6e^(0.25x+3)=26

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