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 = [tex]b^{c}[/tex]
So,
Logb A = 3 , then A = [tex]b^{3}[/tex]
Logb C = 2 , then C = [tex]b^{2}[/tex]
Logb D = 5 , then D = [tex]b^{5}[/tex]
Now, According to question
[tex]Logb\frac{D^{2}}{C^{3}A}[/tex]
So, [tex]Logb\frac{(b^{5})^{2}}{(b^{2})^{3}\times b^{3}}[/tex]
Or, [tex]Logb\frac{b^{10}}{b^{6}\times b^{3}}[/tex]
or, [tex]Logb\frac{b^{10}}{b^{9}}[/tex]
Now, since base same So,
[tex]log_{b}b^{10-9}[/tex]
∴ [tex]log_{b}b^{1}[/tex]
Now log property
[tex]log_{b}b[/tex] = 1
Hence The value of given log function is 1 . answer
