Solve 3!*3^x-3*10=540

$$3 ! \times { 3 }^{ x-3 } \times 10=540$$

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

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

$$60\times 3^{x-3}=540$$

Divide both sides by 60.

$$3^{x-3}=9$$

Take the logarithm of both sides of the equation.

$$\log(3^{x-3})=\log(9)$$

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

$$\left(x-3\right)\log(3)=\log(9)$$

Divide both sides by \log(3).

$$x-3=\frac{\log(9)}{\log(3)}$$

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

$$x-3=\log_{3}\left(9\right)$$

Add 3 to both sides of the equation.

$$x=2-\left(-3\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+5$$

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