Algebra Examples

$4^{x + 3} = 2^{2 (x + 1)}$

Step 1

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

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

Step 2

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

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

Step 3

Solve for $x$ .

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Step 3.1

Simplify $2 (x + 3)$ .

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Step 3.1.1

Rewrite.

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

Step 3.1.2

Simplify by adding zeros.

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

Step 3.1.3

Apply the distributive property.

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

Step 3.1.4

Multiply $2$ by $3$ .

$2 x + 6 = 2 (x + 1)$

Step 3.2

Simplify $2 (x + 1)$ .

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Step 3.2.1

Apply the distributive property.

$2 x + 6 = 2 x + 2 \cdot 1$

Step 3.2.2

Multiply $2$ by $1$ .

$2 x + 6 = 2 x + 2$

Step 3.3

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

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Step 3.3.1

Subtract $2 x$ from both sides of the equation.

$2 x + 6 - 2 x = 2$

Step 3.3.2

Combine the opposite terms in $2 x + 6 - 2 x$ .

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Step 3.3.2.1

Subtract $2 x$ from $2 x$ .

$0 + 6 = 2$

Step 3.3.2.2

Add $0$ and $6$ .

$6 = 2$

Step 3.4

Since $6 \neq 2$ , there are no solutions.

No solution