Evaluate: i. log5∜25/625

Question

Evaluate:

 i. \(log5\sqrt[4]{\cfrac{25}{625}}\)

 ii. \(log_{10}\left(\cfrac{12}{15}\right)\)+ \(log_{10}\left(\cfrac{25}{21}\right)\)- \(log_{10}\left(\cfrac{2}{7}\right)\)

iii. \(log_{10}\left(\cfrac{15}{16}\right)\)+ \(log_{10}\left(\cfrac{64}{81}\right)\)-  \(log_{10}\left(\cfrac{20}{27}\right)\)

iv. log₁₀2+16 log₁₀\(\left(\cfrac{16}{15}\right)\)+ 16 log₁₀\(\left(\cfrac{25}{24}\right)\)+ 7 log₁₀\(\left(\cfrac{81}{80}\right)\)

v.  log₁₀\(\left(\cfrac{351}{539}\right)\) + 2 log₁₀\(\left(\cfrac{91}{110}\right)\) - 3 log₁₀\(\left(\cfrac{39}{110}\right)\) 

Answer 1

i. log₅\(\cfrac{\sqrt[4]{25}}{625}\)= = log₅\(\left(\cfrac{(25)^{1/4}}{625}\right)\)