Solve 5^x*3y=0

$$5 ^ { x } \times 3 y = 0$$

Solve for x

$$x\in \mathrm{R}$$

$$y=0$$

Steps Using Definition of Logarithm

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

$$3y\times 5^{x}=0$$

Divide both sides by 3y.

$$5^{x}=0$$

Take the logarithm of both sides of the equation.

$$\log(5^{x})=\log(0)$$

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

$$x\log(5)=\log(0)$$

Divide both sides by \log(5).

$$x=\frac{\log(0)}{\log(5)}$$

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

$$x=\log_{5}\left(0\right)$$

Solve for y

$$y=0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$3\times 5^{x}y=0$$

Divide 0 by 3\times 5^{x}.

$$y=0$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$y=0$$