### Home > CCA2 > Chapter 11 > Lesson 11.1.1 > Problem 11-10

Natural logs and exponential functions with base

*e*are often used in formulas. But many problems can be solved equally well using either a base-10 logarithm or a base-*e*logarithm. Solve each of the following problems, first using thekey (base 10) and then using the key (base *e*) on your calculator. Homework Help ✎10,000(1.08)

= 20,000^{x}30,000(0.8)

= 15,000^{x}Interpret the answer for part (a) if the equation represents an amount of money invested at 8% annual interest.

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

log(1.08^{x}) = log2

*x* · log(1.08) = log2

9.00646832

You should get the same answer using natural logs.

See part (a).

What does *x* represent in this equation?

What does *x* represent in this equation?