Solve for x (y/2)-1=4^(x-1)

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

Rewrite the equation as $4^{x - 1} = \frac{y}{2} - 1$ .

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

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

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

Expand $\ln (4^{x - 1})$ by moving $x - 1$ outside the logarithm.

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

Simplify the left side.

Simplify $(x - 1) \ln (4)$ .

Apply the distributive property.

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

Rewrite $- 1 \ln (4)$ as $- \ln (4)$ .

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

Move all the terms containing a logarithm to the left side of the equation.

$x \ln (4) - \ln (4) - \ln (\frac{y}{2} - 1) = 0$

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

Add $\ln (4)$ to both sides of the equation.

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

Add $\ln (\frac{y}{2} - 1)$ to both sides of the equation.

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

Divide each term in $x \ln (4) = \ln (4) + \ln (\frac{y}{2} - 1)$ by $\ln (4)$ and simplify.

Divide each term in $x \ln (4) = \ln (4) + \ln (\frac{y}{2} - 1)$ by $\ln (4)$ .

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

Simplify the left side.

Cancel the common factor of $\ln (4)$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $\ln (4)$ .

Cancel the common factor.

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

Rewrite the expression.

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