Solve for x 2^(1+2x)=32

$2^{1 + 2 x} = 32$

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

$2^{1 + 2 x} = 2^{5}$

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

$1 + 2 x = 5$

Solve for $x$ .

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

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Subtract $1$ from both sides of the equation.

$2 x = 5 - 1$

Subtract $1$ from $5$ .

$2 x = 4$

Divide each term by $2$ and simplify.

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Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Divide $4$ by $2$ .

$x = 2$

Solve for x 2^(1+2x)=32

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