1. LOGS and LN and e

2. 112x = 102x-1
Log 112x= log 102x-1
2x Log 11= (x-1) log 102 use distrib. Prop.
2x log 11 = x log log 102 group x
-x log xlog 102
2x log 11 – x log 102 = log 102 factor out x
x(2 log 11 -log 102) = log 102 divide
_______________
(2 log 11 -log 102)
_______________
(2 log 11 log 102)

3. 72x = 35x-2
Log 72x = log 35x-2
2x Log 7= (5x-2) log 3 use distrib. Prop.
2x log 7 = 5x log 3 – 2 log 3 group x
-5x log x log 3
2x log 7 – 5x log 3 = log 3
x(2 log 7 – 5 log 3) = log 3
_______________
(2 log 7 – 5 log 3)
_______________
(2 log 7 – 5 log 3)

4. (ln x)2 – 5 ln x + 6 = 0
( Ln x – 3) ( ln x – 2) = 0
ln x - 3 =0 or ln x -2 = 0
ln x= ln x=2
x=e x=e2
e e

5. ex = 72x-3
ln ex = ln 72x-3
x ln e = (2x-3) ln 7
x ln e = x ln 7 – 3 ln 7
-2x ln x ln 7
x ln e – 2x ln 7 = -3 ln 7
x (ln e – 2 ln 7) = -3 ln 7
___________
(ln e – 2 ln 7)
___________
(ln e – 2 ln 7)

6. Change of base formula
Log8 5 =
F(x)= log 6 x =