can you guys help me with the logarithm of a quotient...???? plsssssssssssss.....T_T?

Question

I need it for my report in Math..... I'm just confused.......

Answer 1

The logarithm of a quotient (i.e. log(x/y)) is equal to the difference of the logarithms. So, log(x/y) = log x - log y.

Answer 2

A logarithm (in a given base) represents the exponent that the value would have if the number was written as a power of the base.

e.g.: In base 10, One thousand can be written as 10^3 (ten to power 3); therefore, the Log(base 10) of 1,000 is 3.

Fractions are represented as negative powers (e.g., 1/1000 = 10^-3). The Log(base 10) of 1/1000 is -3.

If a number is the result of a multiplication (a product), its logarithm is the sum of the Logs of the factors.

If C = A*B, then Log(C) = Log(A) + Log(B).
This is equivalent to saying that when multiplying factored representations in the same base, you add the exponents.

Example: x^7 * x^3 = (xxxxxxx)*(xxx) = xxxxxxxxxx = x^10

If a number is a quotient (the result of the division of one term by another), its logarithm is the difference of the Logs of the two terms.

Example: If C = A/B, then Log(C) = Log(A) - Log(B).

This comes from the fact that dividing by B is the same as multiplying by 1/B, and the Log of (1/B) is the inverse of the Log of B.

C = A/B = A*(1/B)
Log(C) = Log(A) + Log(1/B) = Log(A) + [-Log(B)]

This is equivalent to saying that when dividing factored representations in the same base, you subtract the exponents.

x^7 / x^3 = xxxxxxx / xxx = xxxx = x^4

Answer 3

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