Evaluate (y/2)-1=4^(x-1)

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

Step 1

Add $1$ to both sides of the equation.

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $2 (4^{x - 1} + 1)$ .

Apply the distributive property.

$y = 2 \cdot 4^{x - 1} + 2 \cdot 1$

Multiply $2 \cdot 4^{x - 1}$ .

Rewrite $4$ as $2^{2}$ .

$y = 2 \cdot {(2^{2})}^{x - 1} + 2 \cdot 1$

Multiply the exponents in ${(2^{2})}^{x - 1}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y = 2 \cdot 2^{2 (x - 1)} + 2 \cdot 1$

Apply the distributive property.

$y = 2 \cdot 2^{2 x + 2 \cdot - 1} + 2 \cdot 1$

Multiply $2$ by $- 1$ .

$y = 2 \cdot 2^{2 x - 2} + 2 \cdot 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 2^{1 + 2 x - 2} + 2 \cdot 1$

Subtract $2$ from $1$ .

$y = 2^{2 x - 1} + 2 \cdot 1$

Multiply $2$ by $1$ .

$y = 2^{2 x - 1} + 2$