Log Flashcards
(16 cards)
What is the definition of the logarithm of a number to a given base?
The power that the base is raised to equal a given number
How is log10 100 expressed mathematically?
log10 100 = 2 is written as 10^2 = 100
What is the difference between common logarithm and natural logarithm?
log10 (x) = 1 (x) while lne (x) = 1 (x)
What is a transcendental number?
A special number that cannot be defined exactly, like pi
If y = e^x, what is x in terms of logarithms?
x = loge y = ln y
What is the rule for the sum of logarithms?
log a + log b = log (ab)
What is the rule for the difference of logarithms?
log a - log b = log (a/b)
What is the power rule of logarithms?
a log b = log b^a
How can logb a be expressed in terms of logarithms of different bases?
logb a = logc a / logc b OR logb a x logc b = logc a
What is the relationship between loga b and natural logarithms?
loga b = loge b / loge a
What does the equation logab = c imply?
a^c = b
What is the value of ln 1?
0
What is the value of loga a?
1
What is the implication of loga x = loga y?
x = y
What does aloga(x) equal?
x
How can -logb a be expressed?
-logb a = logb 1/a OR log1/b a
