. Have a doubt in LOGARITHM!!!!!! IT is said that as we cannot express ZERO and NEGATIVE NUMBERS as a power of a positive number,the logarithms of zero and negative numbers are not defined.WHY IS IT SO?can u give an example???AM VERY CONFUSED....

Dear student

Your question is:

Why log is not defined for negative numbers?

Ans. By the def. of log:   .

take an example:

if x = 3 and a = 2, then y = 3² = 9

if x = 3 and a = -2, then y = 3^-2 = 1/9

if x = -3 and a = 2, then y = (-3)²  = 9

if x = -3 and a = -2, then y = (-3)^-2  = 1/9

Thus if x and a are +ve or -ve, y is always positive.

therefore y can not be negative in any case and so log for negative number is not defined. 

Remark: Log of negative numbers are defined in term of complex number which is not included in course.

Hope it resolve your quarry.

Regards

Team Topper