Trigonometry Examples

$\log (14) = \log (x - 5) + \log (5)$

Step 1

Simplify $\log (x - 5) + \log (5)$ .

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Step 1.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (14) = \log ((x - 5) \cdot 5)$

Step 1.2

Apply the distributive property.

$\log (14) = \log (x \cdot 5 - 5 \cdot 5)$

Step 1.3

Simplify the expression.

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Step 1.3.1

Move $5$ to the left of $x$ .

$\log (14) = \log (5 \cdot x - 5 \cdot 5)$

Step 1.3.2

Multiply $- 5$ by $5$ .

$\log (14) = \log (5 x - 25)$

Step 2

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

$x = \frac{39}{5}$

Step 3