SOLUTION: Log 2 (3x-2)- Log 2 (x-5)=4
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Question 448288: Log 2 (3x-2)- Log 2 (x-5)=4
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Log 2 (3x-2)- Log 2 (x-5)=4
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Log 2 (3x-2)- Log 2 (x-5)=4
log2 (3x-2)/(x-5)=4 (division rule for logs)
convert to exponential form (base(2) raised to log of number(4) is equal to number((3x-2)/(x-5)
2^4=(3x-2)/(x-5)
16=3x^2-17x+10
3x^2-17x-6=0
solve by quadratic formula below:
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a=3, b=-17, c=-6
x=[-(-17)ħsqrt((-17)^2-4*3*-6)]/2*3
x=[17ħsqrt(361)]6
x=(17ħ19)/6
x=36/6=6
or
x=-2/6=-1/3 (reject, (x-5)>0)
Check: with x=6
log2(3*6-2)-log2(6-5)
log2(16)-log2(1)=4-0=4
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