Solve for x 80=5(1/2)^(-2x-5)

$80 = 5 {(\frac{1}{2})}^{- 2 x - 5}$

Step 1

Rewrite the equation as $5 {(\frac{1}{2})}^{- 2 x - 5} = 80$ .

$5 {(\frac{1}{2})}^{- 2 x - 5} = 80$

Step 2

Divide each term in $5 {(\frac{1}{2})}^{- 2 x - 5} = 80$ by $5$ and simplify.

Divide each term in $5 {(\frac{1}{2})}^{- 2 x - 5} = 80$ by $5$ .

$\frac{5 {(\frac{1}{2})}^{- 2 x - 5}}{5} = \frac{80}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 {(\frac{1}{2})}^{- 2 x - 5}}{5} = \frac{80}{5}$

Divide ${(\frac{1}{2})}^{- 2 x - 5}$ by $1$ .

${(\frac{1}{2})}^{- 2 x - 5} = \frac{80}{5}$

Simplify the expression.

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

$\frac{1^{- 2 x - 5}}{2^{- 2 x - 5}} = \frac{80}{5}$

One to any power is one.

$\frac{1}{2^{- 2 x - 5}} = \frac{80}{5}$

Simplify the right side.

Divide $80$ by $5$ .

$\frac{1}{2^{- 2 x - 5}} = 16$

Step 3

Move $2^{- 2 x - 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2^{- (- 2 x - 5)} = 16$

Step 4

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

$2^{- (- 2 x - 5)} = 2^{4}$

Step 5

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

$- (- 2 x - 5) = 4$

Step 6

Solve for $x$ .

Simplify $- (- 2 x - 5)$ .

Apply the distributive property.

$- (- 2 x) - - 5 = 4$

Multiply.

Multiply $- 2$ by $- 1$ .

$2 x - - 5 = 4$

Multiply $- 1$ by $- 5$ .

$2 x + 5 = 4$

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

Subtract $5$ from both sides of the equation.

$2 x = 4 - 5$

Subtract $5$ from $4$ .

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5$

Solve for x 80=5(1/2)^(-2x-5)

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