Solve for x log of x^2=2

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

Step 1

Write in exponential form.

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, $b = 10$ , $x = x^{2}$ , and $y = 2$ .

$b = 10$

$x = x^{2}$

$y = 2$

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

$10^{2} = x^{2}$

Step 2

Solve for $x$ .

Rewrite the equation as $x^{2} = 10^{2}$ .

$x^{2} = 10^{2}$

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| x | = | 10 |$

Solve for $x$ .

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x = \pm | 10 |$

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$x = \pm 10$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 10$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 10$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 10, - 10$

Solve for x log of x^2=2

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