Math Help

Archive for April, 2007

Question: Help With Math Homework. (logarithms)?

directions:
Use the rules of logarithms to show that the following are equivalent:
a) -4log3 + log 3 = log(1/27)
b) ln (16/3x) = 4ln2 – (ln3 + lnx)

Answer: a)
-4 * log3 + log3 = log(1/27)
FACTOR OUT log3
log3 * (-4 + 1) = log(1/27)
log3 * (-3) = log(1/27)
-3 * log3 = log(1/27)
APPLY RULE: B * logA = logA^B on left side
log3^(-3) = log(1/27)
APPLY RULE: for negative exponents
log(1/(3^3)) = log(1/27)
log(1/27) = log(1/27)

b)
ln(16/3x) = 4ln2 – (ln3 + lnx)
APPLY RULE: ln(m/n) = ln(m) – ln(n)
ln(16/3x) = ln(16) – ln(3x)
APPLY RULE: ln(mn) = ln(m) + ln(n)
ln(16/3x) = ln(16) – (ln3 + lnx)
SINCE 16 = 2^4
ln(16/3x) = ln(2^4) – (ln3 + lnx)
APPLY RULE: ln(A^B) = BlnA
ln(16/3x) = 4ln2 – (ln3 + lnx)

Algebra – Logarithms – Product Rule of Logs Intuitive Math Help Log Number