What is a log answer?
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.
What is a log of 4?
The value of log 4 to the base 4 is equal to unity. Antilogarithm of logarithmic value of 4 is equal to 4.
What is log value?
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. because. 102 = 100.
Why is Log used?
Logarithms are a convenient way to express large numbers. (The base-10 logarithm of a number is roughly the number of digits in that number, for example.) Slide rules work because adding and subtracting logarithms is equivalent to multiplication and division. (This benefit is slightly less important today.)
What are the log rules?
The rules apply for any logarithm logbx, except that you have to replace any occurence of e with the new base b. The natural log was defined by equations (1) and (2)….Basic rules for logarithms.
| Rule or special case | Formula |
|---|---|
| Quotient | ln(x/y)=ln(x)−ln(y) |
| Log of power | ln(xy)=yln(x) |
| Log of e | ln(e)=1 |
| Log of one | ln(1)=0 |
Why is log used?
How does a log work?
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. The logarithm of a product is the sum of the logarithms of the factors. The logarithm of the ratio or quotient of two numbers is the difference of the logarithms.
How do you solve log powers?
Use the power property of logarithms to simplify the logarithm on the left. Divide both sides by log 4 to get x by itself. Use a calculator to evaluate the logarithms and the quotient. You could have used either the common log or the natural log with the example above.
How is a logarithm used to answer a question?
So a logarithm answers a question like this: The logarithm tells us what the exponent is! In that example the “base” is 2 and the “exponent” is 3: So the logarithm answers the question: (for one number to become another number) ? Example: What is log10(100) ? So an exponent of 2 is needed to make 10 into 100, and:
How to find the value of log 3?
If log 2 = 03.301 and log 3 = 0.4771, find the value of log3 72 5 Q.3. If x, y and z are the sides of a right angled triangle, where ‘z’ is the hypotenuse, then find the value of (1/log x+z y) + (1/log x-z y) Here x, y and z are the sides of a right angled triangle, so z 2 = x 2 + y 2. Q.4.
What does ” log ” mean without a base 10?
Note: On our calculators, ” log ” (without any base) is taken to mean ” log base 10 “. So, for example ” log 7 ” means ” log107 “. 1. Expand as the sum of 2 logarithms. Note 2: This question is not the same as `log_7 x`, which means “log of x to the base `7`”, which is quite different. 2. Using your calculator, show that )= log20− log5.
Which is the logarithm of the number log10100?
log10100 = 2 is equivalent to 102= 100 where 10 is the base, 2 is the logarithm (i.e., the exponent or power) and 100 is the number. Using natural logs (logeor ln): Carrying all numbers to 5 significant figures, ln 30 = 3.4012 is equivalent to e3.4012= 30 or 2.71833.4012= 30
So a logarithm answers a question like this: The logarithm tells us what the exponent is! In that example the “base” is 2 and the “exponent” is 3: So the logarithm answers the question: (for one number to become another number) ? Example: What is log10(100) ? So an exponent of 2 is needed to make 10 into 100, and:
Do you condense the logs on both sides of the equation?
Given Simplify the exponent (still referring to the leftmost term) Then, condense the logs on both sides of the equation. Use the Quotient Rule on the left and Product Rule on the right. 10 10 ), it’s okay to set them equal to each other. Dropping the logs and just equating the arguments inside the parenthesis.
When do you write ln instead of log E?
When the base is e, ln is usually written, rather than log e. log 2, the binary logarithm, is another base that is typically used with logarithms. If for example: Each of the mentioned bases are typically used in different applications. Base 10 is commonly used in science and engineering, base e in math and physics, and base 2 in computer science.
What does the log of a number mean?
This means that the log of a number is the number that a fixed base has to be raised to in order to yield the number. Conventionally, log implies that base 10 is being used, though the base can technically be anything. When the base is e, ln is usually written, rather than log e. log 2, the binary logarithm, is another base