1, a common logarithmic formula.

2. [Formula Description]? The formula of changing base is a common logarithmic operation formula in high school mathematics, which can be used together with other logarithmic operation formulas. In the calculation, the calculation difficulty is often reduced, and the logarithmic operation in the middle and high schools can be solved faster.

Four inferences of the formula for changing the bottom

1, true position adjustment, reciprocal value.

2, the base is really a number, and the logarithm is added with a negative sign.

3, the bottom is really the same power, and the value is as usual.

4. The logarithmic ratio with the same base can be changed with the same base.

For example:

Loga(b) represents the logarithm based on b.

The bottoming formula is: log (a) (b) = log (c) (b)/log (c) (a) (both a and c are greater than zero and not equal to 1).

deductive procedure

Let a = n x, b = n y (n > 0, and n is not 1), such as: log (10) (5) = log (5)/log (5) (10).

Then log (a) (b) = log (n x) (n y)

According to the basic formula of logarithm: log (a) (m n) = nloga (m) and the basic formula log (a n) m =1/n× log (a) m.

Easy to obtain:

Log (n x) (n y) = ylog (n x) (n) = y/x logarithm (n) (n) = y/x.

X = log (n) (a) and y = log (n) (b) can be obtained from a = n x and b = n y.

Then there is: log (a) (b) = log (n x) (n y) = log (n) (b)/log (n) (a).

Proof: log(a)(b)=log(n)(b)/log(n)(a)

For example: log (a) (c) * log (c) (a) = log (c) (c)/log (c) (a) * log (c) (a) = log (c) (c) =1.

Equation 2: log(a)(b)= 1/log(b)(a) is proved as follows:

Log(a)(b)= log(b)(b)/log(b)(a)- take the logarithm based on b.

Log (b) (b) =1=/log (b) (a) can also be converted into: log(a)(b)×log(b)(a)= 1.