Algebra Examples

$(2^{2 x} + 2) (2^{3 x - 7}) = 2^{25}$

Step 1

Simplify $(2^{2 x} + 2) (2^{3 x - 7})$ .

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Step 1.1

Apply the distributive property.

$2^{2 x} \cdot 2^{3 x - 7} + 2 \cdot 2^{3 x - 7} = 2^{25}$

Step 1.2

Multiply $2^{2 x}$ by $2^{3 x - 7}$ by adding the exponents.

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Step 1.2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 x + 3 x - 7} + 2 \cdot 2^{3 x - 7} = 2^{25}$

Step 1.2.2

Add $2 x$ and $3 x$ .

$2^{5 x - 7} + 2 \cdot 2^{3 x - 7} = 2^{25}$

Step 1.3

Multiply $2$ by $2^{3 x - 7}$ by adding the exponents.

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Step 1.3.1

Multiply $2$ by $2^{3 x - 7}$ .

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Step 1.3.1.1

Raise $2$ to the power of $1$ .

$2^{5 x - 7} + 2^{1} \cdot 2^{3 x - 7} = 2^{25}$

Step 1.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{5 x - 7} + 2^{1 + 3 x - 7} = 2^{25}$

Step 1.3.2

Subtract $7$ from $1$ .

$2^{5 x - 7} + 2^{3 x - 6} = 2^{25}$

Step 2

Raise $2$ to the power of $25$ .

$2^{5 x - 7} + 2^{3 x - 6} = 33554432$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution