Precalculus Examples

$\log_{4} (3 x - 5) = 0$

Step 1

Rewrite $\log_{4} (3 x - 5) = 0$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$4^{0} = 3 x - 5$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Rewrite the equation as $3 x - 5 = 4^{0}$ .

$3 x - 5 = 4^{0}$

Step 2.2

Anything raised to $0$ is $1$ .

$3 x - 5 = 1$

Step 2.3

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.3.1

Add $5$ to both sides of the equation.

$3 x = 1 + 5$

Step 2.3.2

Add $1$ and $5$ .

$3 x = 6$

Step 2.4

Divide each term in $3 x = 6$ by $3$ and simplify.

Tap for more steps...

Step 2.4.1

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Step 2.4.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Step 2.4.3

Simplify the right side.

Tap for more steps...

Step 2.4.3.1

Divide $6$ by $3$ .

$x = 2$