Solve for x 4^(x+3)=(1/2)^x

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

Step 1

Apply the product rule to $\frac{1}{2}$ .

$4^{x + 3} = \frac{1^{x}}{2^{x}}$

Step 2

One to any power is one.

$4^{x + 3} = \frac{1}{2^{x}}$

Step 3

Move $2^{x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4^{x + 3} = 2^{- x}$

Step 4

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

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

Step 5

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

$2 (x + 3) = - x$

Step 6

Solve for $x$ .

Simplify $2 (x + 3)$ .

Start simplifying.

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

Simplify by adding zeros.

$2 (x + 3) = - x$

Apply the distributive property.

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

Multiply $2$ by $3$ .

$2 x + 6 = - x$

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

Add $x$ to both sides of the equation.

$2 x + 6 + x = 0$

Add $2 x$ and $x$ .

$3 x + 6 = 0$

Subtract $6$ from both sides of the equation.

$3 x = - 6$

Divide each term in $3 x = - 6$ by $3$ and simplify.

Divide each term in $3 x = - 6$ by $3$ .

$\frac{3 x}{3} = \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 6}{3}$

Divide $x$ by $1$ .

$x = \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$x = - 2$

Solve for x 4^(x+3)=(1/2)^x

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