Home > A2C > Chapter 12 > Lesson 12.5.2 > Problem12-206

12-206.

Natural logs and exponential functions in base e are often used in formulas. For many problems you can use either the $\boxed{LOG}$ or the $\boxed{ LN}$ key on your calculator. Solve each of the following problems, first using base $10 \text{ logs}$ and then using natural logs.

1. $10,000\left(1.08\right)^{x} = 20,000$

$\operatorname{log}\left(1.08^{x}\right) = \operatorname{log}2$

$x · \operatorname{log}(1.08) = \operatorname{log}2$

$9.00646832$

You should get the same answer using natural logs.

2. $30,000\left(0.8\right)^{x} = 15,000$

See part (a).

3. Interpret the answer for part (a) if the equation represents an amount of money invested at $8\%$ annual interest.

What does x represent in this equation?

4. Interpret the answer to part (b) if the equation represents the price paid for a car that depreciates at $20\%$ per year.

What does $x$ represent in this equation?