SOLUTION: could anyone please help me with these they are really confusing log7 + log (n - 2) = log 6n log5m = log5125 logy =1/4log16 +1/2log49 log6(b2 + 2) + log62 = 2 log3(5

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Question 32597: could anyone please help me with these they are really confusing
log7 + log (n - 2) = log 6n
log5m = log5125
logy =1/4log16 +1/2log49
log6(b2 + 2) + log62 = 2
log3(5x+5) - log3(x2 - 1) = 0

Answer by mukhopadhyay(490) (Show Source):
You can put this solution on YOUR website!
log7 + log (n - 2) = log 6n
=> log 7(n-2) = log 6n (using property log a + log b = log(ab))
=> 7(n-2) = 6n => 7n-14 = 6n => n=14;
..........
log5m = log5125
=> 5m = 5125
=> m = 5125/5 => m = 1025
..................
logy =1/4log16 +1/2log49
=> log y = Log [16^(1/4)] + log [49^(1/2)]
=> log y = log 2 + log 7
=> log y = log 14
=> y = 14;
................
log6(b^2 + 2) + log62 = 2
=> log(base6) [2(b^2+2)] = 2
=> 2(b^2+2) = 6^2 = 36
=> b^2 + 2 = 18
=> b^2 = 16
=> b = 4 or b=-4;
..................
log3(5x+5) - log3(x^2 - 1) = 0
=> log(base3) [(5x+5)/(x^2-1)] = 0
=> [(5x+5)/(x^2-1)] = 1
=> 5/(x-1) = 1
=> x-1 = 5
=> x=6