Calculus Examples

$\ln (345) = 2 x + 3$

Step 1

Rewrite the equation as $2 x + 3 = \ln (345)$ .

$2 x + 3 = \ln (345)$

Step 2

Subtract $3$ from both sides of the equation.

$2 x = \ln (345) - 3$

Step 3

Divide each term in $2 x = \ln (345) - 3$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x = \ln (345) - 3$ by $2$ .

$\frac{2 x}{2} = \frac{\ln (345)}{2} + \frac{- 3}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\ln (345)}{2} + \frac{- 3}{2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (345)}{2} + \frac{- 3}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Rewrite $\frac{\ln (345)}{2}$ as $\frac{1}{2} \ln (345)$ .

$x = \frac{1}{2} \ln (345) + \frac{- 3}{2}$

Step 3.3.1.2

Simplify $\frac{1}{2} \ln (345)$ by moving $\frac{1}{2}$ inside the logarithm.

$x = \ln (345^{\frac{1}{2}}) + \frac{- 3}{2}$

Step 3.3.1.3

Move the negative in front of the fraction.

$x = \ln (345^{\frac{1}{2}}) - \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (345^{\frac{1}{2}}) - \frac{3}{2}$

Decimal Form:

$x = 1.42177220 \dots$