Let logb A= 3; logb C = 2; logb D=5What is the value of logb D^2/C^3A
Accepted Solution
A:
Answer: The value of given log function is 1 . Step-by-step explanation:Given as :Logb A = 3Logb C = 2Logb D = 5Now 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] = 1Hence The value of given log function is 1 . answer