Which of the following is not a property of logarithms?
A. log(A - B) = logA/logB
B. logA + logB = logAB
C. xloga = loga^x
D. log(b) b^x = x
(A)
it's log(A/B) = logA - logB
logA/logB = logAB
oops. that's logBA
To determine which of the options is not a property of logarithms, let's examine each one in order:
A. log(A - B) = logA/logB
To verify if this is a property of logarithms, we can test it with some numbers. Let's assume A = 4 and B = 2.
log(4 - 2) = log(2) = 0.3010
log(4)/log(2) = 2/0.3010 ≈ 6.644
Since the values on both sides of the equation are not equal, option A is not a property of logarithms.
B. logA + logB = logAB
To check this property, let's take A = 10 and B = 100.
log(10) + log(100) = 1 + 2 = 3
log(10*100) = log(1000) = 3
The values on both sides of the equation are equal, so option B is a valid property of logarithms.
C. xloga = loga^x
To test this property, let's substitute values for x and a. We'll use x = 2 and a = 10.
2log(10) = log(10^2) = log(100) = 2
Since the values are equal, option C is a valid property of logarithms.
D. log(b) b^x = x
Let's substitute values for b and x in this property. We'll use b = 10 and x = 2.
log(10) (10^2) = 2
Since the values are equal, option D is also a valid property of logarithms.
After examining all the options, we find that option A, log(A - B) = logA/logB, is not a property of logarithms.