Precalculus Examples

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

Step 1

Simplify $3 \log (x)$ by moving $3$ inside the logarithm.

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

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x^{3} = x^{3}$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

$x = x$

Step 3.2

Solve for $x$ .

Tap for more steps...

Step 3.2.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.2.1.1

Subtract $x$ from both sides of the equation.

$x - x = 0$

Step 3.2.1.2

Subtract $x$ from $x$ .

$0 = 0$

Step 3.2.2

Since $0 = 0$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$