# Thread: Common Logarithm Questions I don't understand

1. ## Common Logarithm Questions I don't understand

I don't know if they threw in a couple words somewhere,but maybe someone else can help me understand.

The question: Which of the following statements with regard to the logarithm is true?

1. The integers to the left of the decimal point in the common logarithm are called the mantissa.
2. Every common logarithm has three parts: a characteristic, a mantissa, and a fractional exponent.
3. The logarithm of a root of a number is equal to the logarithm of the number multiplied by the index of the root.
4. in the formula A=a^y, y is the logarithm of A to the base a.

I answered 1. But thats wrong, so can someone help me out a little.
Number 4 seems the second part is gibberish, I understand the first part but dunno if the second part is true, is it a true logarithmic form?

Question 2: In the natural system of logarithms, which of the following statements are true?

1. If the logarithm is positive, the antilogarithm is less then 1.
2. If the antilogarithm falls in the interval 1 to 10, the logarithm will be in the interval 0 to 1.
3. If the logarithm is in the interval 0 to 2.3025851 the antilogarithm will be in the interval 1 to 10
4. The base of the natural system of logarithms is called the mantissa.
5. The base of the natural system of logarithms is called the characteristic.
6. The base of the natural system of logarithms is equal to the square root of the base of the common system of logarithms.

I know the answer #2 is incorrect.

Having read the book, and the Wikipedia I am just completely lost

2. Originally Posted by Dangousity
4. in the formula A=a^y, y is the logarithm of A to the base a.

I answered 1. But thats wrong, so can someone help me out a little.
Number 4 seems the second part is gibberish, I understand the first part but dunno if the second part is true, is it a true logarithmic form?
Addressing this question, a common form for logarithmic functions is as follows:

Say you have the equation:

$y = a^x$

To change this into a logarithm you have:

$\log_a{y} = x$

Logarithms help us to get x out of an exponent to make it easier to work with. So #4 makes sense to me since it is just that formula applied.

Hope this clears up some confusion.