Algebra Examples

$5^{x - 2} - 5^{3} = 500$

Step 1

Rewrite $5^{x - 2}$ as $5^{x} \cdot 5^{- 2}$ .

$5^{x} \cdot 5^{- 2} - 5^{3} = 500$

Step 2

Simplify each term.

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Step 2.1

Raise $5$ to the power of $3$ .

$5^{x - 2} - 1 \cdot 125 = 500$

Step 2.2

Multiply $- 1$ by $125$ .

$5^{x - 2} - 125 = 500$

Step 3

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

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Step 3.1

Add $125$ to both sides of the equation.

$5^{x - 2} = 500 + 125$

Step 3.2

Add $500$ and $125$ .

$5^{x - 2} = 625$

Step 4

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

$5^{x - 2} = 5^{4}$

Step 5

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

$x - 2 = 4$

Step 6

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

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Step 6.1

Add $2$ to both sides of the equation.

$x = 4 + 2$

Step 6.2

Add $4$ and $2$ .

$x = 6$