Trigonometry Examples

$e^{7 x + 4} = 10$

Step 1

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

$\ln (e^{7 x + 4}) = \ln (10)$

Step 2

Expand the left side.

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Step 2.1

Expand $\ln (e^{7 x + 4})$ by moving $7 x + 4$ outside the logarithm.

$(7 x + 4) \ln (e) = \ln (10)$

Step 2.2

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

$(7 x + 4) \cdot 1 = \ln (10)$

Step 2.3

Multiply $7 x + 4$ by $1$ .

$7 x + 4 = \ln (10)$

Step 3

Subtract $4$ from both sides of the equation.

$7 x = \ln (10) - 4$

Step 4

Divide each term in $7 x = \ln (10) - 4$ by $7$ and simplify.

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Step 4.1

Divide each term in $7 x = \ln (10) - 4$ by $7$ .

$\frac{7 x}{7} = \frac{\ln (10)}{7} + \frac{- 4}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{\ln (10)}{7} + \frac{- 4}{7}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (10)}{7} + \frac{- 4}{7}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x = \frac{\ln (10)}{7} - \frac{4}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (10)}{7} - \frac{4}{7}$

Decimal Form:

$x = - 0.24248784 \dots$