SOLUTION: solve the equation: 1)3 ln 3x =6 2) ln √x+7 =4 3)ln(3x-4) =ln(4)-ln(x-1) 4) log(x^2-6)=1 5) (9/7)^x=6^1-x

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve the equation: 1)3 ln 3x =6 2) ln √x+7 =4 3)ln(3x-4) =ln(4)-ln(x-1) 4) log(x^2-6)=1 5) (9/7)^x=6^1-x      Log On


   

Question 670111: solve the equation:
1)3 ln 3x =6
2) ln √x+7 =4
3)ln(3x-4) =ln(4)-ln(x-1)
4) log(x^2-6)=1
5) (9/7)^x=6^1-x
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
solve the equation:
1)3 ln 3x =6
ln3x=6/3=2
e^2=3x
x=e^2/3
x≈2.463
..
2) ln √(x+7)=4
e^4=√(x+7)
square both sids
e^8=x+7
x=e^8-7
x≈2973.9578-7
x≈2966.9578
..
3)ln(3x-4) =ln(4)-ln(x-1)
ln(3x-4) =ln(4/(x-1))
3x-4=4/(x-1)
(3x-4)(x-1)=4
3x^2-7x+4=4
3x^2-7x=0
x(3x-7)=0
x=0 (reject, (x-1)>0)
or
x=7/3
..
4) log(x^2-6)=1
10^1=x^2-6
x^2-16=0
(x+4)(x-4)=0
x=-4
or
x=4
..
5) (9/7)^x=6^(1-x)
xlog(9/7)=(1-x)log6
x/(1-x)=log6/log(9/7)=7.1296
x=7.1296-7.1296x
8.1296x=7.1296
x=7.1296/8.1296
x≈0.8770