Algebra Examples

$2^{\log_{2} (8 x - 5)} \leq 6$

Step 1

Convert the inequality to an equality.

$2^{\log_{2} (8 x - 5)} = 6$

Step 2

Solve for $x$ .

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Step 2.1

Exponentiation and log are inverse functions.

$8 x - 5 = 6$

Step 2.2

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

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Step 2.2.1

Add $5$ to both sides of the equation.

$8 x = 6 + 5$

Step 2.2.2

Add $6$ and $5$ .

$8 x = 11$

Step 2.3

Divide each term in $8 x = 11$ by $8$ and simplify.

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Step 2.3.1

Divide each term in $8 x = 11$ by $8$ .

$\frac{8 x}{8} = \frac{11}{8}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $8$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{11}{8}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{11}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{8}$

Decimal Form:

$x = 1.375$

Mixed Number Form:

$x = 1 \frac{3}{8}$

Step 4