Precalculus Examples

$6 e^{5 x - 6} - 4 = 50$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Add $4$ to both sides of the equation.

$6 e^{5 x - 6} = 50 + 4$

Step 1.2

Add $50$ and $4$ .

$6 e^{5 x - 6} = 54$

Step 2

Divide each term in $6 e^{5 x - 6} = 54$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 e^{5 x - 6} = 54$ by $6$ .

$\frac{6 e^{5 x - 6}}{6} = \frac{54}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 e^{5 x - 6}}{6} = \frac{54}{6}$

Step 2.2.1.2

Divide $e^{5 x - 6}$ by $1$ .

$e^{5 x - 6} = \frac{54}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $54$ by $6$ .

$e^{5 x - 6} = 9$

Step 3

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

$\ln (e^{5 x - 6}) = \ln (9)$

Step 4

Expand the left side.

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Step 4.1

Expand $\ln (e^{5 x - 6})$ by moving $5 x - 6$ outside the logarithm.

$(5 x - 6) \ln (e) = \ln (9)$

Step 4.2

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

$(5 x - 6) \cdot 1 = \ln (9)$

Step 4.3

Multiply $5 x - 6$ by $1$ .

$5 x - 6 = \ln (9)$

Step 5

Add $6$ to both sides of the equation.

$5 x = \ln (9) + 6$

Step 6

Divide each term in $5 x = \ln (9) + 6$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 x = \ln (9) + 6$ by $5$ .

$\frac{5 x}{5} = \frac{\ln (9)}{5} + \frac{6}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{\ln (9)}{5} + \frac{6}{5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (9)}{5} + \frac{6}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (9)}{5} + \frac{6}{5}$

Decimal Form:

$x = 1.63944491 \dots$