Solve for x 64^(4x)=16^(x+3)

$64^{4 x} = 16^{x + 3}$

Step 1

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

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

Step 2

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

$3 (4 x) = 2 (x + 3)$

Step 3

Solve for $x$ .

Multiply $4$ by $3$ .

$12 x = 2 (x + 3)$

Simplify $2 (x + 3)$ .

Apply the distributive property.

$12 x = 2 x + 2 \cdot 3$

Multiply $2$ by $3$ .

$12 x = 2 x + 6$

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

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

$12 x - 2 x = 6$

Subtract $2 x$ from $12 x$ .

$10 x = 6$

Divide each term in $10 x = 6$ by $10$ and simplify.

Divide each term in $10 x = 6$ by $10$ .

$\frac{10 x}{10} = \frac{6}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{6}{10}$

Divide $x$ by $1$ .

$x = \frac{6}{10}$

Simplify the right side.

Cancel the common factor of $6$ and $10$ .

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$x = \frac{2 \cdot 3}{2 \cdot 5}$

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 5}$

Rewrite the expression.

$x = \frac{3}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{5}$

Decimal Form:

$x = 0.6$

Solve for x 64^(4x)=16^(x+3)

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