Change Of Base Formula

Change of Base Formula

Logarithms can be changed by using the Change of Base Formula, as its name suggests. The only buttons on a scientific calculator are “log” and “ln”. In addition, we know that “log” refers to a logarithm of base 10 and “ln” refers to a logarithm of base e. Any other base other than 10 or e cannot be used to calculate the logarithm of a number. By using this formula, one can change the base from e to 10 and from 10 to e. Several logarithm problems can also be solved using it.

What is Change of Base?

By using this formula, one can write a logarithm of a number with a given base as the ratio of two logarithms with the same base but a different base from the original logarithm. Logarithms have this property.

Change of Base Formula Derivation

As its name implies, the Change of Base Formula alters the base of a logarithm. In the scientific calculator, there are only two buttons: log and ln, where log represents a base 10 logarithm and ln represents a base e logarithm. Nevertheless, these buttons do not calculate for values other than 10 and e. The difficulty can be resolved by changing the basic formula. In addition, it is used to solve a variety of logarithm difficulties.

Solved Examples

Students can subscribe to the Extramarks website for having access to various solved examples related to the Change of Base Formula. Along with this, Extramarks also provides students with various learning tools such as Live Doubt Solving Sessions, Comprehensive Study Materials, Self-Assessment Center, Gamified Learning Experience and much more. These tools help students to excel in their studies and have a bright academic career.

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FAQs (Frequently Asked Questions)

The Change of Base Formula alters the base of a logarithm, as its name implies. There are only two buttons on a scientific calculator: “log” and “ln.” We know that “log” represents a base 10 logarithm and “ln” represents a base e logarithm.

With this formula, the logarithm can be rewritten in terms of another base logarithm. In the evaluation of log, this formula is used that has a different base than 10.

Using this formula, you can use the calculator to compute logarithms with a base of e, e. button. log ⁡ 10 ( ⋅). (⋅). Then, input the operations on the right side of the equation into a calculator:

Using the this formula, logarithms can be converted to any base. Using this calculator, logarithms can be calculated in any base other than 10 and e, since it only has options to calculate logarithms in bases 10 (log button) and e (ln button).