Solve 7.2^x/2=45^

$$\frac{ { 7.2 }^{ x } }{ 2 } = { 45 }^{ }$$

Solve for x

$$x=\log_{7.2}\left(90\right)\approx 2.279445277$$

Steps Using Definition of Logarithm

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

$$\frac{1}{2}\times 7.2^{x}=45$$

Multiply both sides by 2.

$$7.2^{x}=90$$

Take the logarithm of both sides of the equation.

$$\log(7.2^{x})=\log(90)$$

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

$$x\log(7.2)=\log(90)$$

Divide both sides by \log(7.2).

$$x=\frac{\log(90)}{\log(7.2)}$$

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

$$x=\log_{7.2}\left(90\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(7.2)}+\log_{7.2}\left(90\right)$$

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