SOLUTION: Write the expression as a single natural logarithm: 3 IN x

SOLUTION: Write the expression as a single natural logarithm: 3 IN x - 2 In c

Question 1016245: Write the expression as a single natural logarithm:
3 IN x - 2 In c
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe you mean ln for natural log.
in capital letters that's LN.

start with 3 * ln(x) - 2 * ln(c).

3 * ln(x) is equal to ln(x^3).

2 * ln(c) is equal to ln(c^2)

your expression becomes ln(x^3) - ln(c^2)

ln(x^3) - ln(c^2) is equal to ln(x^3/c^2)

you're done.

in general, the properties of logarithms are as follows:

log(a) + log(b) = log(a*b)

log(a) - log(b) = log(a/b)

a * log(b) = log(b^a)

logb(a) = c if and only if b^c = a

you need to study these and become familiar with them or you'll get lost real early.

here's a reference that might help.

http://www.purplemath.com/modules/logrules.htm

here's another one.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut44_logprop.htm

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