Solving Change of Base Formula

The solving change of base formula is known as formulas which it permits us to rework a logarithm by means of the logs that may be is written with different base.

The change of base formula is given by,

Log a x = log b x / log b a

Here, assume that a, b and x are positive where a≠1 and b≠1.

Importance in solving change of base formula:

• Using the change of base formula we can change any base to another base. The most commonly used bases are base 10 and base e.

Log a x = log b x / log b a

• The solving change of base formula is used highly if calculators to assess a log to several base further than 10 or e.
• At the solving change of base formula having the value of x which is superior than zero.
• The log of a number to a given base is the power or an exponent to which the base must be raised in order to produce that number.

Advantages  in using change of base formula:

• Change the numeral bases, like convert  from base 2 to base 10m which is known as base conversion.
• The logarithmic change-of-base formula is applicable regularly in algebra and calculus.
• It is used for varying among the polynomial and normal bases.

solving Examples using change of base formula:


1) Solve  log 816

Solution:

By solving the change of base formula

=> log a x = log b x / log b a

log 8 16 = log 2 16 / log 2 8

=  4 / 3

2) Solve log 918

Solution:

By solving the change of base formula

=> log a x= log b x / log b a

log 9 18 = log 2 18 / log 2 9

= 4.169 / 3.169

= 1.315

3) Solve log 2 5.

Solution:

By solving the change of base formula

=> log a x= log b x / log b

log 2 5 = log 10 5 / log 102

The approximate value of the above expression is solving by,

=0 .6989 / 0.30103

=0 .3494

Practice problems in solving change of base formula :

1) Solve log 3 9 using the change of base formula.

Answer: 2

2) Solve log 10 8 using the change of base formula

Answer: 0 .9030