What happens if log base is less than 1?

If the base is less than 1, the logarithmic function is decreasing. The graph gets close to the y-axis when x is small, but with positive y values instead of negative ones.

Can you take the log of a number less than 1?

General procedure for determining logarithms of numbers less than 1: Determine the mantissa of the number as if it were between 1 and 10, using your L scale. Then subtract the characteristic for the number of places the decimal point of your actual number is to the left of the whole single digit number.

Can you take the log of a positive number?

The argument of a log function can only take positive arguments. In other words, the only numbers you can plug into a log function are positive numbers.

Can the log of a positive number be negative?

The logarithm of a positive number may be negative or zero.

Is the log of a number less than 1 negative?

In fact, the log of a number less than 1 must be negative: Since 0.01 = 10-2, we must have log 0.01 = -2. Also, log 0.001 = -3. Since 1 = 100, we have log 1 = 0.

Why can’t you take a log of a negative number?

The logarithm is the “inverse function” of the exponential function. For any real number , the exponential is always a positive real number. So, if is negative, there is no real number that we could call the logarithm of and have it satisfy the defining equation that works for positive reals.

Why is the log of a decimal negative?

Logs can also be figured for numbers less than one. When a number is a fraction (less than one), then the log is always negative. Why does this work? Because 10-2 is the same as 1/102, which equals 1/100, which equals 0.01!

Why is log of a negative number undefined?

What is the logarithm of a negative number? Since the base b is positive (b>0), the base b raised to the power of y must be positive (by>0) for any real y. So the number x must be positive (x>0). The real base b logarithm of a negative number is undefined.