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

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

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

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

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)=

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

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

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

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

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)]

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)

Write each logarithm in terms of ln 2 and ln 3 27 ln 12

Write each logarithm in terms of ln 2 and ln 5 32 ln 20

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

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

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**

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