Logarithm Value

The logarithmic function F with base c is the inverse of the function

G(x) = cx for c > 0, c != 1. We write F(x) = logc(x). That is,

y = logc(x) if and only if cy = x.

Understanding Expand each Logarithm is always challenging for me but thanks to all math help websites to help me out.

The logarithm of a number base is the power or exponent to which the base must be increased in order to produce that number. For example, the logarithm of 100 to base 10 is 2, because 2 is the power to which ten must be raised to produce 100: 102 = 100, so log10100  = 2.

Problems on logarithmic value:

Find the value of log1/4 1/16

Solution:

From the logarithmic rule, to change the value of the base as 4, log1/4 1/16= -log4 1/16

Change the value of 1/16 as 16, by using the log rules log1/4 1/16= -log4 1/16 = log4 16

Now the question is changed to log4 16

To find the value of log4 16, divide 16 by 4 until we get 1

16/4 = 4
4/4 = 1

So here 2 division are needed, log4 16=2

log1/4 1/16 = 2

Problems on logarithmic value:

Find the value of log25 100

Solution:

To find the value of log25 100, divide 100 by 25 until we get 1

100/25 = 4
4/25 = 0.16

So here 2 division are needed, log25 100=2

Log25 100 = 2

Problems on logarithmic value:

Find the value of log1/8 1/72

Solution:

From the logarithmic rule, to change the value of the base as 8, log1/8 1/72= -log8 1/72

Change the value of 1/72 as 72, by using the log rules log1/8 1/72= -log1/8 1/72 = log8 72

Now the question is changed to log8 72

To find the value of log8 72, divide 72 by 8 until we get 1

72/8 =9
9/8 = 1.125

1.125/8=0.140625

So here 3 division are needed, log1/8 1/72=3

log1/8 1/72 = 3