1. Bell Work Evaluate using the Properties of Exponents
xm * xn = ________
Xm= ________ 4. √x = _______
xn (Rewrite with exponent)
3. (xm)n = __________

2. Quick Review of Logs
logbb= ______
ln e= _______
ln 1 = _______ 1 1

3. Properties of Logarithms
log b (xy) = logbx+logby
logb(x/y) =logbx – logby
logbxp = p logbx
ln (xy) = lnx + lny
ln (x/y) = lnx – lny
lnxp= plnx

4. ln(xy)= lnx + lny logb(xy) = logbx + logby
log7(2x)=
log4(5xy)=
ln (3*2) = ln (5x)= ln (2ab)=
Log35 + log3 2
Ln 3 + ln 2
ln 5 + ln x
Log7 2 + log7 x
ln 2 + ln a + ln b
Log45+ log4x+ log4y

5. ln(x/y) = lnx – lny logb(x/y) = logbx-logby
Log b (a/c) =
Log b (7/x) =
Ln(7/5) =
Ln (a/b)=
Ln (8/y)=

6. Logaxp = plogax ln xp= plnx
Log5x3 =
Ln x5 =
3 log 5x
5 ln x

7. Applying more than one property
log10(5x3y)
log log x + log y
ln √(3x-5) 7
½ ln (3x-5) – ln 7

8. Applying more than one property
log3(3x)½
½ + ½ log3 x
log3 3x½
1+½ log3x

9. Applying more than one property
log 3x2y
log5(x-4)⅗
ln x3y2 z4
ln (__x__) 2
x2 - 1

10. Using properties to condense
2 ln (x+2) – ln x ½
logx + 3 log (x+1)
½ln 3 + ½ln x
⅓[log2x + log2(x-4)]

11. Using properties to condense
log x – log y
4 ln ( x-4) – 2 lnx
log58 - log5t
[4 ln x + 4 ln (x+5)] – 2 ln (x-5)

12. Write each logarithm in terms of ln 2 and ln 327
ln 12

13. Write each logarithm in terms of ln 2 and ln 532
ln 20

14. WITHOUT USING A CALCULATOR find the exact value of the logarithm
log42 + log4 32

15. WITHOUT USING A CALCULATOR find the exact value of the logarithm
3 ln e 4
2log3 81
-log749

16. Evaluate using the calculator
Calculators automatically use a base of 10 when you plug in a logarithm.
When the base is something other than 10, you can still use the calculator but you MUST use the change of base formula.
logax = log x OR ln x
log a ln a
**EITHER WILL WORK**

17. Evaluate using the calculator
log 2 58
log 9 15
log 3 7