What are some good ways for high school students to quickly understand logarithmic calculations?

The essence of logarithm is that a number n is constantly divided by m, and when n is 1, the total number of executions is performed. For example, if 32 is constantly divided by 2, to turn 32 into 1, a total of 5 times must be executed, that is, 2 is the base, log32 = 5, in the same way, 81 is constantly divided by 3, and 81 is to be turned into 1, a total of 4 steps must be executed, that is, log 81 = 4 with 3 as the baseConversely, multiplying 5 2s is 32, and multiplying 4 3s is 81

The above is exactly the opposite of logarithm and power. Therefore, n is constantly divided by 2, and to turn n into 1, logn must be executed a total of times, that is, with 2 as the base, logn(If the base is a positive integer.)

The multiplication of two "original numbers" equals the "original number" corresponding to the "representative number" obtained by adding the "representative number"; The division of the "original number" is equal to the "original number" corresponding to the "representative number" obtained by subtracting the "representative number". That is, these two columns can be used to turn a more complex multiplication and division method into a simpler addition and subtraction method.

The logarithm is the operation to find the exponent, and the logarithm of b with a as the base is to find the power of a is equal to b. The base number is multiplied by a finite order to give a value, and the logarithm is this degree.

The logarithm is used to calculate the number of dimensions.

Symmetrical n dimensions, the addition of dimensions and the multiplication of projections are equivalent.

If the dimensions are not symmetrical, addition cannot be equivalent to multiplication. The fact that space can be simplified is premised on symmetry, i.e., the base is the same.

Logarithm is also one of the inverse operations of the power, because the relationship between the base number and the exponent and the power of the power of the result of the power operation is not as simple as subtraction (subtraction and difference) division (divisor and quotient), so we artificially gave him a definition, and this definition is logarithmic. The essence of logarithm is actually an operation.

Logarithm is the inverse of an exponent, and that's what is written in black and white in middle school math books. Or you can think of logarithms, like trigonometric functions, as elementary functions that require a calculator to find specific values.

Logarithms are just a powerful tool for doing exponential operations. It doesn't make sense to talk about logarithms alone, which are a representation of numbers (existing as an inverse representation of exponents).

First, 2(lg 2) 2 +lg 2 times lg5 extracts the common factor (lg 2)*(2lg 2 +lg5)=(lg 2)*(lg2 +lg5)=lg 2 (uses lg2+lg5=1 ) second, uses 2lg 2=lg2 [(lg 2) 2-lg2+1] = [(lg 2) 2-2lg 2+1] to completely flatten, open the root. Get 1-lg2 combined.

Add one and two to get 1. And one more of your questions is because 3+2 2 is equal to 1 (3-2 2).

1 All of the following are calculated according to the logarithmic nature.

log with 2 base 3 logarithm * log with 3 base 4 log=log with 2 base 4 log=2

ln root number e=1 2

1 of 2 + log with 2 as base, 3 as the power of the logarithm = 2*2 as the log, 2 as the base 3, and the power of the logarithm of 3 = 2*3 = 6

So the answer is 13 2

The image of the properties of logarithmic functions, as well as the images of exponential functions, mainly grasp the ideas of functions and equations, as well as the idea of combining numbers and shapes, the transformation between images, and the derivatives.

Memorize the formula, connect a few more topics, and you're foolproof.

The commonly used logarithmic judgment of the power of the whole digging pin is equal to the power exponent? Don't fight Qili help me explain the explanation thank you?

2. The loga(b) power of a is equal to b, how to reason?