# How does a logarithm work?

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In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

Also know, how are logarithms calculated?

Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.

Also Know, what is the value of log 0? Log 0 is undefined. The result is not a real number, because you can never get zero by raising anything to the power of anything else. You can never reach zero, you can only approach it using an infinitely large and negative power. The real logarithmic function logb(x) is defined only for x>0.

Consequently, what is log10 equal to?

Mathematically, log10(x) is equivalent to log(10, x) . See Example 1. The logarithm to the base 10 is defined for all complex arguments x ≠ 0. log10(x) rewrites logarithms to the base 10 in terms of the natural logarithm: log10(x) = ln(x)/ln(10) .

What is a logarithm in simple terms?

A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.

34 Related Question Answers Found

### What is log2 value?

According to Logarthmic values the value of log2 is 0.3010.

### How are logarithms used in real life?

Using Logarithmic Functions
Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity).

### What is LN equal to?

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.

### What is the value of log?

Common Log base 10 Values Tables
Number (x) log10(x)
log(1) 0
log(2) 0.30103
log(3) 0.477121
log(4) 0.60206

### What is the property of log?

Recall that we use the product rule of exponents to combine the product of exponents by adding: xaxb=xa+b x a x b = x a + b . We have a similar property for logarithms, called the product rule for logarithms, which says that the logarithm of a product is equal to a sum of logarithms.

### How do you eliminate a log?

Examples
1. Start with the equation: For example, log x = log (x - 2) + 3.
2. Rearrange the terms: log x - log (x - 2) = 3.
3. Apply the law of logarithms: log (x/x-2) = 3.
4. Raise both sides to a power of 10: x ÷ (x - 2) = 3.
5. Solve for x: x = 3.

### Is Log same as log10?

Usually log(x) means the base 10 logarithm; it can, also be written as log10(x) . log10(x) tells you what power you must raise 10 to obtain the number x. 10x is its inverse. ln(x) means the base e logarithm; it can, also be written as loge(x) .

### Is the value of log10?

Value of Log 10. The value of log can be either with base 10 or with base e. The log10 10 value is 1 while the value of loge10 or ln(10) is 2.302585.

### Is log10 the same as LN?

No, log10 (x) is not the same as ln(x), although both of these are special logarithms that show up more often in the study of mathematics than any

### What is value of log3?

log3 basically signifies the number raised to 10 that results in 3. therefore 10^0.477 is 3. log3 = 0.477.

### What is a log10 scale?

A logarithmic scale is a nonlinear scale used for a large range of positive multiples of some quantity. It is based on orders of magnitude, rather than a standard linear scale, so the value represented by each equidistant mark on the scale is the value at the previous mark multiplied by a constant.

### Why is it called logarithm?

Logarithms even describe how humans instinctively think about numbers. Logarithms were invented in the 17th century as a calculation tool by Scottish mathematician John Napier (1550 to 1617), who coined the term from the Greek words for ratio (logos) and number (arithmos).

### What is the value of ln 0?

ln(0) = ? The real natural logarithm function ln(x) is defined only for x>0. So the natural logarithm of zero is undefined.

### Why do we use log10?

There are two main reasons to use logarithmic scales in charts and graphs. The first is to respond to skewness towards large values; i.e., cases in which one or a few points are much larger than the bulk of the data. The second is to show percent change or multiplicative factors.

### What is the use of log file?

LOG is the file extension for an automatically produced file that contains a record of events from certain software and operating systems. While they can contain a number of things, log files are often used to show all events associated with the system or application that created them.

### What is the opposite of log?

Logarithms are the "opposite" of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs "undo" exponentials. Technically speaking, logs are the inverses of exponentials. On the left-hand side above is the exponential statement "y = bx".

### What is the inverse of log?

Some functions in math have a known inverse function. The log function is one of these functions. We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log subb(x) is f^-1(y) = b^y.