Solve 9450=350*3^x

$$9450 = 350 \times 3 ^ { x }$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

Divide both sides by 350.

$$\frac{9450}{350}=3^{x}$$

Divide 9450 by 350 to get 27.

$$27=3^{x}$$

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

$$3^{x}=27$$

Take the logarithm of both sides of the equation.

$$\log(3^{x})=\log(27)$$

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

$$x\log(3)=\log(27)$$

Divide both sides by \log(3).

$$x=\frac{\log(27)}{\log(3)}$$

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

$$x=\log_{3}\left(27\right)$$

Solve for x (complex solution)

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

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