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Bell Work
Evaluate using the Properties of Exponents1. xm * xn = ________
2. Xm= ________ 4. √x = _______ xn
(Rewrite with exponent)
3. (xm)n = __________
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Quick Review of Logs
• logbb= ______
• ln e= _______
• ln 1 = _______
1
1
0
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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
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ln(xy)= lnx + lnylogb(xy) = logbx + logby
• log3(5 * 2)=
• log7(2x)=
• log4(5xy)=
ln (3*2) =
ln (5x)=
ln (2ab)=
Log35 + log3 2
Log7 2 + log7 x
Log45+ log4x+ log4y
Ln 3 + ln 2
ln 5 + ln x
ln 2 + ln a + ln b
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ln(x/y) = lnx – lnylogb(x/y) = logbx-logby
• Log 2 (3/5) =
• Log b (a/c) =
• Log b (7/x) =
• Ln(7/5) =
• Ln (a/b)=
• Ln (8/y)=
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Logaxp = plogax ln xp= plnx
• Log5x3 =
• Ln x5 =
3 log 5x
5 ln x
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Applying more than one property
• log10(5x3y)
log 5 + 3 log x + log y
• ln √(3x-5) 7½ ln (3x-5) – ln 7
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Applying more than one property
• log3(3x)½
½ + ½ log3 x
• log3 3x½
1+½ log3x
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Applying more than one property
• log 3x2y
• log5(x-4)⅗
• ln x3y2
z4
• ln (__x__) 2
x2 - 1
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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)]
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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)
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Write each logarithm in terms of ln 2 and ln 3
• ln 6
• ln _2_ 27
• ln 12
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Write each logarithm in terms of ln 2 and ln 5
• ln 10
• ln 5 • 32
• ln 20
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WITHOUT USING A CALCULATOR find the exact value of the logarithm
• log 5 (1/125)
• log 4 (-16)
• log42 + log4 32
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WITHOUT USING A CALCULATORfind the exact value of the logarithm
• 3 ln e 4
• 2log3 81
• -log749
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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**
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Evaluate using the calculator
• log 2 58
• log 9 15
• log 3 7