SOLUTION: Solve fora in log(2a)- 3log2= 1/2log(a-3)

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Question 946643: Solve fora in log(2a)- 3log2= 1/2log(a-3)
Found 2 solutions by MathLover1, lwsshak3:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solve for a in log%282a%29-3log%282%29=+%281%2F2%29log%28a-3%29
log%282%2Aa%29-3log%282%29=+%281%2F2%29log%28a-3%29
log%282a%29-log%282%5E3%29=+log%28%28a-3%29%5E%281%2F2%29%29
log%282a%29-log%288%29=+log%28sqrt%28%28a-3%29%29%29
log%28%282a%2F8%29%29=+log%28sqrt%28%28a-3%29%29%29
log%28%28a%2F4%29%29=+log%28sqrt%28%28a-3%29%29%29 ...if log same, then
a%2F4=+sqrt%28a-3%29...square both sides
%28a%2F4%29%5E2=+%28sqrt%28a-3%29%29%5E2
a%5E2%2F16=+%28a-3%29
a%5E2=+16%28a-3%29
a%5E2=+16a-48
a%5E2-16a%2B48=0...factor completely
a%5E2-4a+-12a%2B48=0...group
%28a%5E2-4a%29+-%2812a-48%29=0
a%28a-4%29+-12%28a-4%29=0
%28a-12%29%28a-4%29+=+0
solutions:
if %28a-12%29+=+0=> a=12
if %28a-4%29+=+0=> a=4

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for a in log(2a)- 3log2= 1/2log(a-3)
log(2a)- 3log2= 1/2log(a-3)
log(2a/(2^3))=log((a-3)^(1/2))
2a(2^3)=(a-3)^(1/2)
16a=√(a-3)
square both sides:
256a^2=a-3
256a^2-a+3=0
b^2-4ac<0
no real solution