Algebra Examples

$\log (x + 48) + \log (x) = 2$

Step 1

Simplify $\log (x + 48) + \log (x)$ .

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Step 1.1

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

$\log ((x + 48) x) = 2$

Step 1.2

Apply the distributive property.

$\log (x \cdot x + 48 x) = 2$

Step 1.3

Multiply $x$ by $x$ .

$\log (x^{2} + 48 x) = 2$

Step 2

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

$x = 2$

Step 3