Trigonometry Examples

$2 \log (x^{2} - 2 x + 5) = 2$

Step 1

Divide both sides by $2$ to remove it from the front of the logarithm.

$\frac{2 \log (x^{2} - 2 x + 5)}{2} = \frac{2}{2}$

Step 2

Simplify each side of the equation.

$\log (x^{2} - 2 x + 5) = 1$

Step 3

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = 10$ , $x = x^{2} - 2 x + 5$ , and $y = 1$ .

$b = 10$

$x = x^{2} - 2 x + 5$

$y = 1$

Step 4

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .

$10 = x^{2} - 2 x + 5$