Trigonometry Examples

$\frac{1}{2} - \log_{16} (x - 3) = \log_{16} (x)$

Step 1

Simplify $\frac{1}{2} - \log_{16} (x - 3)$ .

Tap for more steps...

Step 1.1

To write $- \log_{16} (x - 3)$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} - \log_{16} (x - 3) \cdot \frac{2}{2} = \log_{16} (x)$

Step 1.2

Combine $- \log_{16} (x - 3)$ and $\frac{2}{2}$ .

$\frac{1}{2} + \frac{- \log_{16} (x - 3) \cdot 2}{2} = \log_{16} (x)$

Step 1.3

Combine the numerators over the common denominator.

$\frac{1 - \log_{16} (x - 3) \cdot 2}{2} = \log_{16} (x)$

Step 1.4

Multiply $- \log_{16} (x - 3) \cdot 2$ .

Tap for more steps...

Step 1.4.1

Multiply $2$ by $- 1$ .

$\frac{1 - 2 \log_{16} (x - 3)}{2} = \log_{16} (x)$

Step 1.4.2

Simplify $- 2 \log_{16} (x - 3)$ by moving $2$ inside the logarithm.

$\frac{1 - \log_{16} ({(x - 3)}^{2})}{2} = \log_{16} (x)$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 4$

Step 3