Question

The expression $5^{\log 2}+2^{\log 5}-50^{\log 2}$ equals (Assume base of logarithm as 10.)

• A. $5^{\log 2}$
• B. 1
• C. $5^{\log 2+\log 5}$
• D. 0

Answer 1

Answer: (D)

$2^{{\log }_{10}5}+2^{{\log }_{10}5}=2\cdot 2^{{\log }_{10}5}=2\cdot 2^{{\log }_{10}\left(\frac{10}{2}\right)}=2\cdot 2^{1-{\log }_{10}2}=\frac{4}{2^{{\log }_{10}2}}$ ....(1)
Now, $50^{{\log }_{10}2}=2^{{\log }_{10}50}=2^{{\log }_{10}\left(\frac{100}{2}\right)}=2^{2-{\log }_{10}2}=\frac{4}{2^{{\log }_{10}2}}$.....(2)
$\therefore 5^{\log 2}+2^{\log 5}-50^{\log 2}=0$