Algebra Examples

$\log_{2} (3 x - 7) = 3$

Step 1

Rewrite $\log_{2} (3 x - 7) = 3$ 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 $b^{y} = x$ .

$2^{3} = 3 x - 7$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $3 x - 7 = 2^{3}$ .

$3 x - 7 = 2^{3}$

Step 2.2

Raise $2$ to the power of $3$ .

$3 x - 7 = 8$

Step 2.3

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

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Step 2.3.1

Add $7$ to both sides of the equation.

$3 x = 8 + 7$

Step 2.3.2

Add $8$ and $7$ .

$3 x = 15$

Step 2.4

Divide each term in $3 x = 15$ by $3$ and simplify.

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Step 2.4.1

Divide each term in $3 x = 15$ by $3$ .

$\frac{3 x}{3} = \frac{15}{3}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $3$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{15}{3}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{3}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $15$ by $3$ .

$x = 5$