e^frac{x{4}}=20.5-এর সমাধান করুন

$$e ^ { \frac { x } { 4 } } = 20.5$$

Solve for x

$$x=\ln(176610.0625)\approx 12.081699545$$

Steps Using Definition of Logarithm

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

$$e^{\frac{1}{4}x}=20.5$$

Take the logarithm of both sides of the equation.

$$\log(e^{\frac{1}{4}x})=\log(20.5)$$

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

$$\frac{1}{4}x\log(e)=\log(20.5)$$

Divide both sides by \log(e).

$$\frac{1}{4}x=\frac{\log(20.5)}{\log(e)}$$

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

$$\frac{1}{4}x=\log_{e}\left(20.5\right)$$

Multiply both sides by 4.

$$x=\frac{\ln(\frac{41}{2})}{\frac{1}{4}}$$

Solve for x (complex solution)

$$x=\ln(176610.0625)+i\times 8\pi n_{1}$$

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