Solve 50,000=7.7e^.14x

$$50,000 = 7.7 e ^ { .14 x }$$

Solve for x

$$x=\frac{50\ln(500000)-50\ln(77)}{7}\approx 62.703985397$$

Steps Using Definition of Logarithm

Divide both sides by 7.7.

$$\frac{50000}{7.7}=e^{0.14x}$$

Expand \frac{50000}{7.7} by multiplying both numerator and the denominator by 10.

$$\frac{500000}{77}=e^{0.14x}$$

Swap sides so that all variable terms are on the left hand side.

$$e^{0.14x}=\frac{500000}{77}$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.14x})=\log(\frac{500000}{77})$$

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

$$0.14x\log(e)=\log(\frac{500000}{77})$$

Divide both sides by \log(e).

$$0.14x=\frac{\log(\frac{500000}{77})}{\log(e)}$$

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

$$0.14x=\log_{e}\left(\frac{500000}{77}\right)$$

Divide both sides of the equation by 0.14, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(\frac{500000}{77})}{0.14}$$

Solve for x (complex solution)

$$x=\frac{i\times 100\pi n_{1}}{7}+\frac{50\ln(500000)}{7}-\frac{50\ln(77)}{7}$$

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