Algebra Examples

$P (x) = 2^{5 x + 1} - 8^{2 x - 3}$

Step 1

Set $2^{5 x + 1} - 8^{2 x - 3}$ equal to $0$ .

$2^{5 x + 1} - 8^{2 x - 3} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Move $- 8^{2 x - 3}$ to the right side of the equation by adding it to both sides.

$2^{5 x + 1} = 8^{2 x - 3}$

Step 2.2

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

$2^{5 x + 1} = 2^{3 (2 x - 3)}$

Step 2.3

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

$5 x + 1 = 3 (2 x - 3)$

Step 2.4

Solve for $x$ .

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Step 2.4.1

Simplify $3 (2 x - 3)$ .

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Step 2.4.1.1

Rewrite.

$5 x + 1 = 0 + 0 + 3 (2 x - 3)$

Step 2.4.1.2

Simplify by adding zeros.

$5 x + 1 = 3 (2 x - 3)$

Step 2.4.1.3

Apply the distributive property.

$5 x + 1 = 3 (2 x) + 3 \cdot - 3$

Step 2.4.1.4

Multiply.

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Step 2.4.1.4.1

Multiply $2$ by $3$ .

$5 x + 1 = 6 x + 3 \cdot - 3$

Step 2.4.1.4.2

Multiply $3$ by $- 3$ .

$5 x + 1 = 6 x - 9$

Step 2.4.2

Move all terms containing $x$ to the left side of the equation.

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Step 2.4.2.1

Subtract $6 x$ from both sides of the equation.

$5 x + 1 - 6 x = - 9$

Step 2.4.2.2

Subtract $6 x$ from $5 x$ .

$- x + 1 = - 9$

Step 2.4.3

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

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Step 2.4.3.1

Subtract $1$ from both sides of the equation.

$- x = - 9 - 1$

Step 2.4.3.2

Subtract $1$ from $- 9$ .

$- x = - 10$

Step 2.4.4

Divide each term in $- x = - 10$ by $- 1$ and simplify.

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Step 2.4.4.1

Divide each term in $- x = - 10$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 10}{- 1}$

Step 2.4.4.2

Simplify the left side.

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Step 2.4.4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 10}{- 1}$

Step 2.4.4.2.2

Divide $x$ by $1$ .

$x = \frac{- 10}{- 1}$

Step 2.4.4.3

Simplify the right side.

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Step 2.4.4.3.1

Divide $- 10$ by $- 1$ .

$x = 10$

Step 3