Algebra Examples

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

Step 1

Simplify $\log (x) - \frac{1}{2} \cdot \log (x + 4)$ .

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Step 1.1

Multiply $- \frac{1}{2} \log (x + 4)$ .

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Step 1.1.1

Reorder $\log (x + 4)$ and $\frac{1}{2}$ .

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

Step 1.1.2

Simplify $\frac{1}{2} \log (x + 4)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (x) - \log ({(x + 4)}^{\frac{1}{2}}) = 1$

Step 1.2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

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

Step 2

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

No solution