Solve for x 64^(2x)=16^(x+1)

$64^{2 x} = 16^{x + 1}$

Step 1

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

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

Step 2

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

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

Step 3

Solve for $x$ .

Multiply $2$ by $3$ .

$6 x = 2 (x + 1)$

Simplify $2 (x + 1)$ .

Apply the distributive property.

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

Multiply $2$ by $1$ .

$6 x = 2 x + 2$

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

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

$6 x - 2 x = 2$

Subtract $2 x$ from $6 x$ .

$4 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$

Solve for x 64^(2x)=16^(x+1)

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