Finite Math Examples

$8^{7 x} = 64$

Step 1

Subtract $64$ from both sides of the equation.

$8^{7 x} - 64 = 0$

Step 2

Add $64$ to both sides of the equation.

$8^{7 x} = 64$

Step 3

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

$8^{7 x} = 8^{2}$

Step 4

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

$7 x = 2$

Step 5

Divide each term in $7 x = 2$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 x = 2$ by $7$ .

$\frac{7 x}{7} = \frac{2}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{2}{7}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{7}$