Solve 2^2x+1-3=29

$$2 ^ { 2 x + 1 } - 3 = 29$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$2^{2x+1}-3=29$$

Add 3 to both sides of the equation.

$$2^{2x+1}=32$$

Take the logarithm of both sides of the equation.

$$\log(2^{2x+1})=\log(32)$$

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

$$\left(2x+1\right)\log(2)=\log(32)$$

Divide both sides by \log(2).

$$2x+1=\frac{\log(32)}{\log(2)}$$

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

$$2x+1=\log_{2}\left(32\right)$$

Subtract 1 from both sides of the equation.

$$2x=5-1$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(2)}+2$$

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