isi-entrance 2013 Q6

isi-entrance · India 4 marks Laws of Logarithms Solve a Logarithmic Equation

If $\log _ { 10 } x = 10 ^ { \log _ { 100 } 4 }$ then $x$ equals
(A) $4 ^ { 10 }$
(B) 100
(C) $\log _ { 10 } 4$
(D) none of the above

(B) Let $y = \log _ { 10 } x$. Then $\log _ { 10 } y = \log _ { 100 } 4$. Hence $y = 2$.

If $\log _ { 10 } x = 10 ^ { \log _ { 100 } 4 }$ then $x$ equals\\
(A) $4 ^ { 10 }$\\
(B) 100\\
(C) $\log _ { 10 } 4$\\
(D) none of the above