Solve 50e^0,035x=200

$$50 e ^ { 0,035 x } = 200$$

Solve for x

$$x=\frac{400\ln(2)}{7}\approx 39.608410318$$

Steps Using Definition of Logarithm

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

$$50e^{0,035x}=200$$

Divide both sides by 50.

$$e^{0,035x}=4$$

Take the logarithm of both sides of the equation.

$$\log(e^{0,035x})=\log(4)$$

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

$$0,035x\log(e)=\log(4)$$

Divide both sides by \log(e).

$$0,035x=\frac{\log(4)}{\log(e)}$$

By the change-of-base formula log(a)/log(b)=log(b,a).

$$0,035x=\log_{e}\left(4\right)$$

Divide both sides of the equation by 0,035, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{2\ln(2)}{0,035}$$