Solve h+9=h+2^x

$$h + 9 = h + 2 ^ { x }$$

Solve for x

$$x=2\log_{2}\left(3\right)$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$h+2^{x}=h+9$$

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

$$2^{x}+h=h+9$$

Subtract h from both sides of the equation.

$$2^{x}=9$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(9)$$

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

$$x\log(2)=\log(9)$$

Divide both sides by \log(2).

$$x=\frac{\log(9)}{\log(2)}$$

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

$$x=\log_{2}\left(9\right)$$

Solve for h (complex solution)

$$h\in \mathrm{C}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{2\pi n_{1}i}{\ln(2)}+2\log_{2}\left(3\right)$$

Solve for x (complex solution)

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

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

Solve for h

$$h\in \mathrm{R}$$

$$x=2\log_{2}\left(3\right)$$