Why is the calculation result: log 10 is the logarithm based on 10 = 1?
We can calculate the value of log_ 10 10 according to the definition of logarithm.
It is known that the base of logarithm is 10.
The true number of the known logarithm is: 10.
According to the definition of logarithm, we can get:
10^0= 1
Therefore, log _1010 =1.
How to calculate log_ 10 10 according to the definition of logarithm?
We need to calculate log_ 10 10 according to the definition of logarithm.
We must first understand the definition of logarithm.
Logarithm is a mathematical operation expressed as log_b(a), where b is the base and a is the real number.
Its definition is: if b x = a, then x=log_b(a).
In this problem, the cardinal number b= 10 and the real number a= 10.
So we can get the equation according to the definition: 10 x = 10.
Now we need to solve this equation and find the value of X.
The calculation result is: x= 1.
So according to the definition of logarithm, log _1010 =1.
What is the definition of logarithm?
Logarithm is a mathematical operation, which is expressed in the form that one number (called true number) can be expressed as the power of another number (called base number). Specifically, if the x power of a is equal to n (a >; 0, and a≠ 1), then the number x is called the logarithm of n with a as the base, and is recorded as x=logaN. Where a is called the base of logarithm and n is called real number.
Logarithm is widely used in mathematics. The following are some common application areas:
What is the application of logarithm in mathematics?
1. Scaling and compressing data: Logarithmic functions can be used to scale and compress data. By taking logarithm, the range of data can be reduced from a larger value to a smaller range, and the smaller value can also be enlarged to a larger range. This is usually used to reduce the dynamic range of data and make it easier to process and analyze.
2. Data smoothing and denoising: Logarithmic function can be used to smooth and denoise data. After logarithmization, larger outliers in the data will be compressed, while smaller changes will be amplified. This helps to smooth the data and reduce the influence of noise.
3. Percentage change and growth rate: Logarithmic function can be used to calculate percentage change and growth rate. By taking logarithm, the exponential growth data can be transformed into linear growth, which makes the change trend easier to observe and analyze.
4. Mathematical modeling and economics: In mathematical modeling and economics, logarithmic functions are often used to describe the growth or decline process, such as population growth and bacterial reproduction. In addition, logarithmic functions are often used to calculate compound interest and evaluate stock prices.
5. Chemistry and physics: In chemistry and physics, logarithmic functions are often used to describe chemical reaction rate, radioactive decay and other processes. In addition, logarithmic function is often used to calculate physical quantities such as loudness and light intensity of sound.
6. Image processing: In image processing, logarithmic function can be used for image enhancement, contrast adjustment and other operations. By taking the logarithm of the pixel value of the image, the dynamic range of the image can be reduced to a manageable range, and the contrast and clarity of the image can be enhanced at the same time.