SOLUTION: If a=log4 of 7 and b=log7 of 5, then in terms of a and b, log5 is equal to: a) ab b)(2ab+1)/ab c)2ab/(1+2ab) d)(4b+a)/7 e)a^2-b^2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If a=log4 of 7 and b=log7 of 5, then in terms of a and b, log5 is equal to: a) ab b)(2ab+1)/ab c)2ab/(1+2ab) d)(4b+a)/7 e)a^2-b^2      Log On


   

Question 1197720: If a=log4 of 7 and b=log7 of 5, then in terms of a and b, log5 is equal to:
a) ab
b)(2ab+1)/ab
c)2ab/(1+2ab)
d)(4b+a)/7
e)a^2-b^2
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


a=log%284%2C7%29=log%287%29%2Flog%284%29

b=log%287%2C5%29=log%285%29%2Flog%287%29

Multiply: ab=log%285%29%2Flog%284%29

Solve for log(5): log%285%29=ab%2Alog%284%29

Convert log%284%29 into an expression with log%285%29


log%285%29=2ab-2ablog%285%29

log%285%29%2B2ablog%285%29=2ab

%281%2B2ab%29log%285%29=2ab

log%285%29=2ab%2F%281%2B2ab%29

ANSWER: c)