Trigonometry Examples

$\ln (7 - 2 x) = \ln (3 x + 3)$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$7 - 2 x = 3 x + 3$

Step 2

Solve for $x$ .

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Step 2.1

Move all terms containing $x$ to the left side of the equation.

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Step 2.1.1

Subtract $3 x$ from both sides of the equation.

$7 - 2 x - 3 x = 3$

Step 2.1.2

Subtract $3 x$ from $- 2 x$ .

$7 - 5 x = 3$

Step 2.2

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

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Step 2.2.1

Subtract $7$ from both sides of the equation.

$- 5 x = 3 - 7$

Step 2.2.2

Subtract $7$ from $3$ .

$- 5 x = - 4$

Step 2.3

Divide each term in $- 5 x = - 4$ by $- 5$ and simplify.

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Step 2.3.1

Divide each term in $- 5 x = - 4$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 4}{- 5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 4}{- 5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{4}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{5}$

Decimal Form:

$x = 0.8$