Trigonometry Examples

$e^{4 x - 5} - 7 = 11243$

Step 1

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

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Step 1.1

Add $7$ to both sides of the equation.

$e^{4 x - 5} = 11243 + 7$

Step 1.2

Add $11243$ and $7$ .

$e^{4 x - 5} = 11250$

Step 2

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

$\ln (e^{4 x - 5}) = \ln (11250)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{4 x - 5})$ by moving $4 x - 5$ outside the logarithm.

$(4 x - 5) \ln (e) = \ln (11250)$

Step 3.2

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

$(4 x - 5) \cdot 1 = \ln (11250)$

Step 3.3

Multiply $4 x - 5$ by $1$ .

$4 x - 5 = \ln (11250)$

Step 4

Add $5$ to both sides of the equation.

$4 x = \ln (11250) + 5$

Step 5

Divide each term in $4 x = \ln (11250) + 5$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 x = \ln (11250) + 5$ by $4$ .

$\frac{4 x}{4} = \frac{\ln (11250)}{4} + \frac{5}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{\ln (11250)}{4} + \frac{5}{4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (11250)}{4} + \frac{5}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (11250)}{4} + \frac{5}{4}$

Decimal Form:

$x = 3.58203085 \dots$