Trigonometry Examples

$3 \log_{3} (4 x + 7) - 4 = 2$

Step 1

Move all terms not containing $\log_{3} (4 x + 7)$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $4$ to both sides of the equation.

$3 \log_{3} (4 x + 7) = 2 + 4$

Step 1.2

Add $2$ and $4$ .

$3 \log_{3} (4 x + 7) = 6$

Step 2

Divide each term in $3 \log_{3} (4 x + 7) = 6$ by $3$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $3 \log_{3} (4 x + 7) = 6$ by $3$ .

$\frac{3 \log_{3} (4 x + 7)}{3} = \frac{6}{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{3 \log_{3} (4 x + 7)}{3} = \frac{6}{3}$

Step 2.2.1.2

Divide $\log_{3} (4 x + 7)$ by $1$ .

$\log_{3} (4 x + 7) = \frac{6}{3}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $6$ by $3$ .

$\log_{3} (4 x + 7) = 2$

Step 3

Rewrite $\log_{3} (4 x + 7) = 2$ 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 $b^{y} = x$ .

$3^{2} = 4 x + 7$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Rewrite the equation as $4 x + 7 = 3^{2}$ .

$4 x + 7 = 3^{2}$

Step 4.2

Raise $3$ to the power of $2$ .

$4 x + 7 = 9$

Step 4.3

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

Tap for more steps...

Step 4.3.1

Subtract $7$ from both sides of the equation.

$4 x = 9 - 7$

Step 4.3.2

Subtract $7$ from $9$ .

$4 x = 2$

Step 4.4

Divide each term in $4 x = 2$ by $4$ and simplify.

Tap for more steps...

Step 4.4.1

Divide each term in $4 x = 2$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4}$

Step 4.4.2

Simplify the left side.

Tap for more steps...

Step 4.4.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{4}$

Step 4.4.3

Simplify the right side.

Tap for more steps...

Step 4.4.3.1

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 4.4.3.1.1

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4}$

Step 4.4.3.1.2

Cancel the common factors.

Tap for more steps...

Step 4.4.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Step 4.4.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Step 4.4.3.1.2.3

Rewrite the expression.

$x = \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$