Trigonometry Examples

$100 = 8 + 38 \ln (x)$

Step 1

Rewrite the equation as $8 + 38 \ln (x) = 100$ .

$8 + 38 \ln (x) = 100$

Step 2

Move all terms not containing $\ln (x)$ to the right side of the equation.

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Step 2.1

Subtract $8$ from both sides of the equation.

$38 \ln (x) = 100 - 8$

Step 2.2

Subtract $8$ from $100$ .

$38 \ln (x) = 92$

Step 3

Divide each term in $38 \ln (x) = 92$ by $38$ and simplify.

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Step 3.1

Divide each term in $38 \ln (x) = 92$ by $38$ .

$\frac{38 \ln (x)}{38} = \frac{92}{38}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $38$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{38 \ln (x)}{38} = \frac{92}{38}$

Step 3.2.1.2

Divide $\ln (x)$ by $1$ .

$\ln (x) = \frac{92}{38}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $92$ and $38$ .

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Step 3.3.1.1

Factor $2$ out of $92$ .

$\ln (x) = \frac{2 (46)}{38}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $38$ .

$\ln (x) = \frac{2 \cdot 46}{2 \cdot 19}$

Step 3.3.1.2.2

Cancel the common factor.

$\ln (x) = \frac{2 \cdot 46}{2 \cdot 19}$

Step 3.3.1.2.3

Rewrite the expression.

$\ln (x) = \frac{46}{19}$

Step 4

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (x)} = e^{\frac{46}{19}}$

Step 5

Rewrite $\ln (x) = \frac{46}{19}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{\frac{46}{19}} = x$

Step 6

Rewrite the equation as $x = e^{\frac{46}{19}}$ .

$x = e^{\frac{46}{19}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = e^{\frac{46}{19}}$

Decimal Form:

$x = 11.25770329 \dots$