### Home > CCA2 > Chapter 11 > Lesson 11.1.1 > Problem11-10

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 the $\boxed{\text{LOG}}$ key (base $10$) and then using the $\boxed{\text{LN}}$ key (base $e$) on your calculator.

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

log$(1.08^x) =$ log$2$

$x ·$ log$(1.08) =$ log$2$

$9.00646832$

You should get the same answer using natural logs.

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

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 at $20\%$ per year.

What does $x$ represent in this equation?