Algebra Examples

$8 = 2^{5 x + 7}$

Step 1

Rewrite the equation as $2^{5 x + 7} = 8$ .

$2^{5 x + 7} = 8$

Step 2

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

$2^{5 x + 7} = 2^{3}$

Step 3

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

$5 x + 7 = 3$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $7$ from both sides of the equation.

$5 x = 3 - 7$

Step 4.1.2

Subtract $7$ from $3$ .

$5 x = - 4$

Step 4.2

Divide each term in $5 x = - 4$ by $5$ and simplify.

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Step 4.2.1

Divide each term in $5 x = - 4$ by $5$ .

$\frac{5 x}{5} = \frac{- 4}{5}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 4}{5}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{5}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$x = - \frac{4}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{5}$

Decimal Form:

$x = - 0.8$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{5}$

Decimal Form:

$x = - 0.8$