If a = b2 = c3 then log ab = ……………A) 9/2B) 2/9C) 4/9D) 1/3

1.	If a = b2 = c3 then log ab = ……………A) 9/2B) 2/9C) 4/9D) 1/3
Answer» Correct option is (A) 9/2 \(a=b^2=c^3\) \(\Rightarrow log_c\,a=log_c\,b^2=log_cc^3\) (By takin \(log_c)\) \(\Rightarrow log_c\,a=2\,log_c\,b=3\,log_c\,c\) \((\because log\,a^n=n\,log\,a)\) \(\Rightarrow log_c\,a=2\,log_c\,b=3\) \((\because log_c\,c=1)\) \(\therefore log_c\,a=3\,\&\,\,log_c\,b=\frac32\) Now, \(log_c\,ab=log_c\,a+log_c\,b\) \(=3+\frac32\) \(=\frac{9}{2}\) Correct option is A) 9/2

Answer»

Correct option is (A) 9/2

\(a=b^2=c^3\)

\(\Rightarrow log_c\,a=log_c\,b^2=log_cc^3\) (By takin \(log_c)\)

\(\Rightarrow log_c\,a=2\,log_c\,b=3\,log_c\,c\) \((\because log\,a^n=n\,log\,a)\)

\(\Rightarrow log_c\,a=2\,log_c\,b=3\) \((\because log_c\,c=1)\)

\(\therefore log_c\,a=3\,\&\,\,log_c\,b=\frac32\)

Now, \(log_c\,ab=log_c\,a+log_c\,b\)

\(=3+\frac32\) \(=\frac{9}{2}\)

Correct option is A) 9/2

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