What does logarithm mean in science?

logarithm: The power (or exponent) to which one base number must be raised — multiplied by itself — to produce another number. For instance, in the base 10 system, 10 must be multiplied by 10 to produce 100. So the logarithm of 100, in a base 10 system, is 2.

What is the definition of the logarithm with base a?

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.

How is the change of base formula used in solving logarithmic equations?

In order to evaluate logarithms with a base other than 10 or e , we use the change-of-base formula to rewrite the logarithm as the quotient of logarithms of any other base; when using a calculator, we would change them to common or natural logs.

How do you change the base of a number?

Decimal to Other Base System

  1. Step 1 − Divide the decimal number to be converted by the value of the new base.
  2. Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number.
  3. Step 3 − Divide the quotient of the previous divide by the new base.

Why do we use log scale in science?

A logarithmic scale makes it easy to compare values that cover a large range, such as in this map.

What is a logarithmic scale in biology?

logarithmic scale A scale of measurement in which an increase or decrease of one unit represents a tenfold increase or decrease in the quantity measured. Decibels and pH measurements are common examples of logarithmic scales of measurement. A Dictionary of Biology.

Why does change of base formula work?

By the definition of a logarithm, a=br . Now we can take the base x logarithm of both sides of the equation to end up with logx(a)=logx(br) . loga(b)=logx(a)logx(b) . Therefore, the change of base formula works for any number x as long as logx is defined.