How do you expand law of logarithms?

What are the example of logarithms?

For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8. In the same fashion, since 102 = 100, then 2 = log10 100. Logarithms of the latter sort (that is, logarithms with base 10) are called common, or Briggsian, logarithms and are written simply log n.

How do you expand log 3?

What does expanding a logarithm mean?

When you are asked to expand log expressions, your goal is to express a single logarithmic expression into many individual parts or components. This process is the exact opposite of condensing logarithms because you compress a bunch of log expressions into a simpler one.

What is logarithmic function give at least 3 example?

Using Logarithmic Functions

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). Let’s look at the Richter scale, a logarithmic function that is used to measure the magnitude of earthquakes.

What are the 7 rules of logarithms?

Rules of Logarithms
  • Rule 1: Product Rule. The logarithm of the product is the sum of the logarithms of the factors.
  • Rule 2: Quotient Rule. …
  • Rule 3: Power Rule. …
  • Rule 4: Zero Rule. …
  • Rule 5: Identity Rule. …
  • Rule 6: Inverse Property of Logarithm. …
  • Rule 7: Inverse Property of Exponent. …
  • Rule 8: Change of Base Formula.

How do you expand and condense logarithms?

How do you use the properties of logarithms to expand?

How do you expand logs with LN?

How many types of logarithms are there?

Two kinds of logarithms are often used in chemistry: common (or Briggian) logarithms and natural (or Napierian) logarithms. The power to which a base of 10 must be raised to obtain a number is called the common logarithm (log) of the number. The power to which the base e (e = 2.718281828…….)

How do you solve logarithms?

To solve a logarithm, start by identifying the base, which is “b” in the equation, the exponent, which is “y,” and the exponential expression, which is “x.” Then, move the exponential expression to one side of the equation, and apply the exponent to the base by multiplying the base by itself the number of times …

What is Antilogarithm with example?

Scientific definitions for antilogarithm

The number whose logarithm is a given number. For example, the logarithm of 1,000 (103) is 3, so the antilogarithm of 3 is 1,000. In algebraic notation, if log x = y, then antilog y = x.

What are the 4 laws of logarithmic functions?

Logarithm Rules or Log Rules
  • There are four following math logarithm formulas: ● Product Rule Law:
  • loga (MN) = loga M + loga N. ● Quotient Rule Law:
  • loga (M/N) = loga M – loga N. ● Power Rule Law:
  • IogaMn = n Ioga M. ● Change of base Rule Law:

How do you solve logarithms without a calculator?

What is log10 equal to?

The natural log function of 10 is denoted as “loge 10”. It is also known as the log function of 10 to the base e. The natural log of 10 is also represented as ln(10) The value of loge 10 is equal to 2.302585. loge 10 = ln (10) = 2.302585.

How do you calculate logarithms by hand?

What is the logarithm rule?

Is log always base 10?

A logarithm can have any positive value as its base, but logs with two particular bases are generally regarded as being more useful than the others: the “common” log with a base of ten, and the “natural” log with a base of the number e.

What are logarithms useful for?

Logarithms are defined as the solutions to exponential equations and so are practically useful in any situation where one needs to solve such equations (such as finding how long it will take for a population to double or for a bank balance to reach a given value with compound interest).

What is the easiest way to learn logarithms?

What are the 3 properties of logarithms?

Logarithm Base Properties
  • Product rule: am. an=a. m+n
  • Quotient rule: am/an = a. m-n
  • Power of a Power: (am)n = a. mn