Precalculus Examples

$\log (x) \cdot \log (x) - 2 \log (x) = 3$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (x) \log (x)$ .

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Step 1.1.1

Raise $\log (x)$ to the power of $1$ .

$\log^{1} (x) \log (x) - 2 \log (x) = 3$

Step 1.1.2

Raise $\log (x)$ to the power of $1$ .

$\log^{1} (x) \log^{1} (x) - 2 \log (x) = 3$

Step 1.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\log (x)}^{1 + 1} - 2 \log (x) = 3$

Step 1.1.4

Add $1$ and $1$ .

$\log^{2} (x) - 2 \log (x) = 3$

Step 1.2

Simplify $- 2 \log (x)$ by moving $2$ inside the logarithm.

$\log^{2} (x) - \log (x^{2}) = 3$

Step 2

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

$x \approx 0.1$

Step 3