SOLUTION: Solve the following equations. Show your steps. If the answer is irrational, give both an exact value and a decimal approximation. 3log(3y+2) = log(3y+2)

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Question 410461: Solve the following equations. Show your steps. If the answer is irrational, give both an exact value and a decimal approximation.
3log(3y+2) = log(3y+2) - log7
( log(5x-6) / logx ) = 2
3^2x = 9^x+2
HELP PLEASE!!!!!
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
3log(3y+2) = log(3y+2) - log7
( log(5x-6) / logx ) = 2
3^2x = 9^x+2
..
3log(3y+2)=log(3y+2)-log7
3log(3y+2)-log(3y+2)+log7=0
2log(3y+2)+log7=0
log(3y+2)^2(7)=0
convert to exponential form
10^0=(3y+2)^2(7)=1
(9y^2+12y+4)(7)=1
63y^2+84y+28=1
63y^2+84y+27=0
21y^2+28y+9=0
solving by quadratic formula below:
..

..
a=21,b=28,c=9
y=(-28+-sqrt(28^2-4*21*9))/2*21
y=(-28+-5.2915)42
y=-33.2915/42,-22.7085?42
y=-.7927 (reject, because (3y+2)<0 with this solution
y=-.5407
ans:
y=-.5407..
..
(log(5x-6)/logx)=2
log(5x-6)=2logx
log(5x-6)-2logx=0
log(5x-6)/x^2=0
convert to exponential form
10^0=(5x-6)/x^2=1
x^2-5x+6=0
solve by factoring
(x-3)(x-2)=0
x-3=0
x=3
x-2=0
x=2
ans:
x=3 or x=2
..
3^2x=9^x+2
3^2x=(3^2)^x+2
3^2x=3^2x+4
no solution (left-hand side not equal to right-hand side)

SOLUTION: Solve the following equations. Show your steps. If the answer is irrational, give both an exact value and a decimal approximation. 3log(3y+2) = log(3y+2) - log7 ( log(5x-6) /