Solve 2.73pi^x=2978

$$2.73 \pi ^ { x } = 2978$$

Solve for x

$$x=\log_{\pi }\left(\frac{297800}{273}\right)\approx 6.11035467$$

Steps Using Definition of Logarithm

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

$$2.73\pi ^{x}=2978$$

Divide both sides of the equation by 2.73, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\pi ^{x}=\frac{297800}{273}$$

Take the logarithm of both sides of the equation.

$$\log(\pi ^{x})=\log(\frac{297800}{273})$$

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

$$x\log(\pi )=\log(\frac{297800}{273})$$

Divide both sides by \log(\pi ).

$$x=\frac{\log(\frac{297800}{273})}{\log(\pi )}$$

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

$$x=\log_{\pi }\left(\frac{297800}{273}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(\pi )}+\log_{\pi }\left(\frac{297800}{273}\right)$$

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