Solve 7(1/3)^x=63

$$7 ( \frac { 1 } { 3 } ) ^ { x } = 63$$

Solve for x

$$x=-2$$

Steps Using Definition of Logarithm

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

$$7\times \left(\frac{1}{3}\right)^{x}=63$$

Divide both sides by 7.

$$\left(\frac{1}{3}\right)^{x}=9$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{1}{3}\right)^{x})=\log(9)$$

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

$$x\log(\frac{1}{3})=\log(9)$$

Divide both sides by \log(\frac{1}{3}).

$$x=\frac{\log(9)}{\log(\frac{1}{3})}$$

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

$$x=\log_{\frac{1}{3}}\left(9\right)$$

Solve for x (complex solution)

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

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