How would you solve this equation?
log(ab)=log(a)*log(b)
a=30, b=60
Does the it appear that this is a true statement? Why?
The equation is not true. Consider a=10, b=1
log(10*1)= log10 *log1
and since the log of 1 is zero, this makes the log of 10 equal to zero, so it is nonsense.
Try log(ab)=log a+ log b
other than the obvious of
a=1, b=1, i found some that come very close.
I was so intrigued by the question that I actually went ahead and made up a short computer program to test this.
This is in a very archaic language called "BASIC", but I am sure some of the tutors will recognize it
FOR A = .01 TO 100 STEP .01
FOR B = .01 TO 100 STEP .01
LS = LOG(A*B)/LOG(10)
RS = LOG(A)*LOG(B)/(LOG(10)*LOG(10)
IF ABS(LS-RS) < .00001 THEN PRINT A,B
NEXT B
NEXT A
I got a = .28 and b= 2.27 to have an error of less than .00001 between the left side and the right side of your equation.
of course a=2.27 and b=.28 will also work within that margin of error.
To solve this equation and determine whether it is true or not, we need to substitute the given values of a and b into the equation and compare both sides.
The equation is: log(ab) = log(a) * log(b)
Substituting a = 30 and b = 60, we get:
log(30 * 60) = log(30) * log(60)
Now, to determine if this equation is true, we need to find the values on both sides of the equation.
On the left side, we calculate the logarithm of the product of a and b. Using logarithmic properties, we can simplify this as follows:
log(30 * 60) = log(1800)
On the right side, we calculate the product of the logarithms of a and b:
log(30) * log(60)
Now, we can use a calculator to find the values for both sides of the equation:
log(1800) ≈ 3.25527
log(30) ≈ 1.47712
log(60) ≈ 1.77815
log(30) * log(60) ≈ 1.47712 * 1.77815 ≈ 2.62385
Comparing the values, we see that log(1800) ≈ 3.25527 is not equal to log(30) * log(60) ≈ 2.62385. Therefore, the equation does not hold true for these particular values of a and b.
Hence, it can be concluded that the given statement is not true for a = 30 and b = 60.