Solve 2(pi^x)=7*63

$$2 ( \pi ^ { x } ) = 7 \cdot 63$$

Solve for x

$$x=\log_{\pi }\left(\frac{441}{2}\right)\approx 4.7136864$$

Steps Using Definition of Logarithm

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

$$2\pi ^{x}=441$$

Divide both sides by 2.

$$\pi ^{x}=\frac{441}{2}$$

Take the logarithm of both sides of the equation.

$$\log(\pi ^{x})=\log(\frac{441}{2})$$

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

$$x\log(\pi )=\log(\frac{441}{2})$$

Divide both sides by \log(\pi ).

$$x=\frac{\log(\frac{441}{2})}{\log(\pi )}$$

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

$$x=\log_{\pi }\left(\frac{441}{2}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\pi )}+\log_{\pi }\left(\frac{441}{2}\right)$$

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