SOLUTION: 17) If log 3 = 1.4 and log 5 = 3.6, log 25/3= a) 8.6 b) -0.8 c) 3.4 d) 5.8 e) 6.2

Algebra ->  Trigonometry-basics -> SOLUTION: 17) If log 3 = 1.4 and log 5 = 3.6, log 25/3= a) 8.6 b) -0.8 c) 3.4 d) 5.8 e) 6.2       Log On


   

Question 122531: 17) If log 3 = 1.4 and log 5 = 3.6, log 25/3=

a) 8.6
b) -0.8
c) 3.4
d) 5.8
e) 6.2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%29=3.6 Start with the second equation


2%2Alog%285%29=7.2 Multiply both sides by 2


log%285%5E2%29=7.2 Rewrite the left side using the identity y%2Alog%28x%29=log%28x%5Ey%29


log%2825%29=7.2 Square 5 to get 25


So let's make our third equation be: log%2825%29=7.2


log%2825%2F3%29 Start with the given expression


log%2825%29-log%283%29 Expand the expression using log%28a%2Fb%29=log%28a%29-log%28b%29


7.2-1.4 Replace log%2825%29 with 7.2 ( remember log%2825%29=7.2). Replace log%283%29 with 1.4 ( remember this was given: log%283%29=1.4).


5.8 Subtract


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Answer:
So log%2825%2F3%29=5.8

This means that the answer is D)