CPM Homework Help : CCA2 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 the $\boxed{\text{LOG}}$ key (base $10$ ) and then using the $\boxed{\text{LN}}$ key (base $e$ ) on your calculator.

$10{,}000(1.08)^x = 20{,}000$
Hint (a):
log $(1.08^x) =$ log $2$
More Help (a):
$x ·$ log $(1.08) =$ log $2$
Answer (a):
$9.00646832$
You should get the same answer using natural logs.

$30{,}000(0.8)^x = 15{,}000$
Hint (b):
See part (a).

Interpret the answer for part (a) if the equation represents an amount of money invested at $8\%$ annual interest.
Hint (c):
What does $x$ represent in this equation?
Interpret the answer for part (b) if the equation represents the price paid for a car that depreciates at $20\%$ per year.
Hint (d):
What does $x$ represent in this equation?