CPM Homework Help : INT3 Problem 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.

$10{,}000\left(1.08\right)^{x} = 20{,}000$
Hint (a):
$\text{log}\left(1.08^{x}\right) = \text{log}2$
More Help (a):
$x · \text{log}\left(1.08\right) = \text{log}2$
Answer (a):
$\approx9.00646832$
You should get the same answer using natural logs.

$30{,}000\left(0.8\right)^{x} = 15{,}000$
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 $20\%$ per year.
Hint (d):
What does $x$ represent in this equation?