Function/equation logarithmic

• Jun 15th 2006, 07:14 AM
kbryant05
Function/equation logarithmic
Hi I have a few I am stumped on in my wonderful challenge of Algebra.

First Problem is:

Use the compound interest formulas
A=P(1 + r over n)^nt and A=Pe^rt

Suppose that you have \$14,000 to invest. Which investment yields the greater return over 10 years: 7% compounded monthly or 6.85% compounded continuously?

Second Problem:
find the domain of each logarithmic function.
F(x)=log(3-X)

Third Problem:
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents.

9^x = 1 over 27
• Jun 15th 2006, 10:40 AM
ThePerfectHacker
Quote:

Originally Posted by kbryant05

Second Problem:
find the domain of each logarithmic function.
F(x)=log(3-X)

Third Problem:
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents.

9^x = 1 over 27

Forgive me for not doing the first problem (interest problems make me angry).

2)The logarithm $y=\log x$ its domain is, $x>0$ thus in the problem $y=\log (3-x)$ thus, $3-x>0$ thus, $x<3$

3)
$9^x=\frac{1}{27}$
Note, $9=3^2,27=3^3$ thus,
$(3^2)^x=\frac{1}{3^3}$ use exponents rule,
$3^{2x}=3^{-3}$
Thus,
$2x=-3$
Thus,
$x=-1.5$