1. Tardigrade
  2. Question
  3. Mathematics
  4. The expression 5 log 2+2 log 5-50 log 2 equals (Assume base of logarithm as 10.)

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Continuity and Differentiability

Solution:

$ 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 $