Solve 3(2^x)-2=19

$$3 ( 2 ^ { x } ) - 2 = 19$$

Solve for x

$$x=\log_{2}\left(7\right)\approx 2.807354922$$

Steps Using Definition of Logarithm

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

$$3\times 2^{x}-2=19$$

Add 2 to both sides of the equation.

$$3\times 2^{x}=21$$

Divide both sides by 3.

$$2^{x}=7$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(7)$$

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

$$x\log(2)=\log(7)$$

Divide both sides by \log(2).

$$x=\frac{\log(7)}{\log(2)}$$

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

$$x=\log_{2}\left(7\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(7\right)$$

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