Algebra Examples

$8^{x - 2} - 2^{3} = 56$

Step 1

Simplify each term.

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Step 1.1

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

$8^{x - 2} - 1 \cdot 8 = 56$

Step 1.2

Multiply $- 1$ by $8$ .

$8^{x - 2} - 8 = 56$

Step 2

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

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Step 2.1

Add $8$ to both sides of the equation.

$8^{x - 2} = 56 + 8$

Step 2.2

Add $56$ and $8$ .

$8^{x - 2} = 64$

Step 3

Create equivalent expressions in the equation that all have equal bases.

$8^{x - 2} = 8^{2}$

Step 4

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x - 2 = 2$

Step 5

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

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Step 5.1

Add $2$ to both sides of the equation.

$x = 2 + 2$

Step 5.2

Add $2$ and $2$ .

$x = 4$