TO STUDY FOR FINALS:
3 Laws of Logarithms:
1. logbxy = logbx + logby
"The logarithm of a product is equal to the sumof the logarithms of each factor."
2. logbxy= logbx − logby
"The logarithm of a quotient is equal to the logarithm of the numeratorminus the logarithm of the denominator."
3. logb x n = n logbx
"The logarithm of a power of x is equal to the exponent of that power times the logarithm of x."
Problems to solve with Log:
a) log ab/c
b) ln (sin²x ln x)
c) ln (a2x − 1 b5x + 1 )´
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Answers:
Rewriting with Log Laws
a) log a + log b − log c
b)ln sin²x + ln ln x
= 2ln sin x + ln ln x
c) ln a2x − 1 + ln b5x + 1
= (2x − 1) ln a + (5x + 1)ln b
Remember: logb (bx) = x
More problems with Log:
log2 (2m) = ?
log3 (1/9).
log2 (.25) = ?
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