Question

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

Answer 1

Answer:

The value of given log function is 1 .

Step-by-step 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

$Logb\frac{D^{2}}{C^{3}A}$

So, $Logb\frac{(b^{5})^{2}}{(b^{2})^{3}\times b^{3}}$

Or, $Logb\frac{b^{10}}{b^{6}\times b^{3}}$

or, $Logb\frac{b^{10}}{b^{9}}$

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