Question

Let logb A= 3; logb C = 2; logb D=5
What is the value of logb D^2/C^3A

Answer 1

The value of given log function is 1 .

Explanation:

Given as :

Logb A = 3

Logb C = 2

Logb D = 5

Now from log property

if , Logb x = c , then x =
`b^(c)`

So,

Logb A = 3 , then A =
`b^(3)`

Logb C = 2 , then C =
`b^(2)`

Logb D = 5 , then D =
`b^(5)`

Now, According to question

`Logb(D^(2))/(C^(3)A)`

So,
`Logb((b^(5))^(2))/((b^(2))^(3)* b^(3))`

Or,
`Logb(b^(10))/(b^(6)* b^(3))`

or,
`Logb(b^(10))/(b^(9))`

Now, since base same So,

`log_(b)b^(10-9)`

∴
`log_(b)b^(1)`

Now log property

`log_(b)b` = 1

Hence The value of given log function is 1 . answer