Basic Math Examples

$625 = 5^{6 - 2 m}$

Step 1

Rewrite the equation as $5^{6 - 2 m} = 625$ .

$5^{6 - 2 m} = 625$

Step 2

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

$5^{6 - 2 m} = 5^{4}$

Step 3

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

$6 - 2 m = 4$

Step 4

Solve for $m$ .

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Step 4.1

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

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Step 4.1.1

Subtract $6$ from both sides of the equation.

$- 2 m = 4 - 6$

Step 4.1.2

Subtract $6$ from $4$ .

$- 2 m = - 2$

Step 4.2

Divide each term in $- 2 m = - 2$ by $- 2$ and simplify.

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Step 4.2.1

Divide each term in $- 2 m = - 2$ by $- 2$ .

$\frac{- 2 m}{- 2} = \frac{- 2}{- 2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 2 m}{- 2} = \frac{- 2}{- 2}$

Step 4.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 2}{- 2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 2$ by $- 2$ .

$m = 1$