Solve 2^y+1-384=0

$$2 ^ { y + 1 } - 384 = 0$$

Solve for y

$$y=\log_{2}\left(3\right)+6\approx 7.584962501$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$2^{y+1}-384=0$$

Add 384 to both sides of the equation.

$$2^{y+1}=384$$

Take the logarithm of both sides of the equation.

$$\log(2^{y+1})=\log(384)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$\left(y+1\right)\log(2)=\log(384)$$

Divide both sides by \log(2).

$$y+1=\frac{\log(384)}{\log(2)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$y+1=\log_{2}\left(384\right)$$

Subtract 1 from both sides of the equation.

$$y=\log_{2}\left(384\right)-1$$

Solve for y (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(3\right)+6$$

$$n_{1}\in \mathrm{Z}$$