### Home > INT3 > Chapter 10 > Lesson 10.3.3 > Problem10-184

10-184.

Natural logs (written $\text{log}_{e}\left(x\right)$ or $\text{ln} \left(x\right)$) and exponential expressions with base $e$ are often used in formulas. Many problems can be solved equally well using either a base-$10$ logarithm or a natural logarithm. Solve each of the following problems, first using the $\boxed{\text{LOG}}$ key (base $10$) and then using the $\boxed{\text{LN}}$ key (base $e$) on your calculator.

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

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

$x · \text{log}\left(1.08\right) = \text{log}2$

$9.00646832$

You should get the same answer using natural logs.

1. $30,000\left(0.8\right)^{x} = 15,000$

See part (a).

1. 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?

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

What does $x$ represent in this equation?