write as a single logarithm: 2 ln x - 3 ln y + 1/3 ln z

Solve: |2x-1| < 9

|2x-1|<9
-9 < 2x-1 < 9
-9+1 < 2x-1+1 < 9+1
-8 < 2x < 10
-8/2 < 2x/2 < 10/2
-4 < x < 5

Simplify: 4a-3[2y+6(a-3y)-5a]

4a-3[2y+6(a-3y)-5a]=
4a-3[2y+6a-18y-5a]=
4a-3[a-16y]=
4a-3a+48y=
a+48y

Solve: ln(x+1)-ln(x-2)=ln(2)

Kayla has 80 coins in her bank. They are all dimes and nickels. She ha four times as many dimes as nickels. How much money does she have in her bank?

x+4x=80

5x=80

x=16

so she has 16 nickels (and so 64 dimes)

therefore she has 64*0.1+16*0.05 i.e. $7.20

Simplify this algebraic fraction: 25x^4* y /( 10 x y -15 x y)

Express 9x^2-42x+49 in the form (ax+b)^2 where a and b are constants.