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Expanding and Condensing Logarithms Expand each logarithm. Justify each step by stating logarithm property used. Level 2: 1) log 6 u v 2) log 5 3 a 3) log 7 54 4) log 4 u6 5) log (a ⋅ b) 6) log 5 6 7 Level 3: 7) log 4 x3 8) log 6 (3 ⋅ 11)6 9) log 6 (ab3) 10) log 4 (a ⋅ b ⋅ c) 11) log 5 (10 ⋅ 11 3) 12) log 7 (x ⋅ y)6 Level 4: 13) log ...
Expand each logarithm. 1) log (x4 y) 6 2) log 5 (z2x) 3) log 5 (x4y3) 4) log 6 (ab3) 2 5) log (62 7) 2 6) log 4 (6 × 72) 3 7) log 7 (114 8) 2 8) log 9 (xy5) 6 Condense each expression to a single logarithm. 9) 5log 3 11 + 10log 3 6 10) 6log 9 z + 1 2 × log 9 x 11) 3log 4 z + 1 3 × log 4 x12) log 6 c + 1 2 × log 6 a + 1 2 × log 6 b 13) 6log ...
. = logbX – logbY. logb(XY) = logbX + logbY Power Rule for Logarithms. Quotient Rule for Logarithms. Product Rule for Logarithms. The following examples show how to expand logarithmic expressions using each of the rules above. Example 1. Expand log2493 . log2493 = 3 • log249 . The answer is 3 • log249. Use the Power Rule for Logarithms.
Logarithms: Expand, Condense, Properties, Equations. Expand each logarithm. ln ( x 6 y 3) log ( x ⋅ y ⋅ z 3) 8. log 9 ( 33. 7 )4. log 7 ( 3 x. )3. log ( a 6 b 5) 8. log ( 4 63 ⋅ 113) 11) log ( c 5 3 a 6 ) 12) ln ( 52. 2 )5. 13) log ( x 3. y )6. 5. 14) log. 4 ( 73 3 2) 15) log ( u ⋅ v ⋅ w. 2 2) 16) log ( 123 ⋅ 7)6. 9. ( 5 3. 17) log c a. 9 )
Worksheet by Kuta Software LLC Pre-Calculus 3.3: Condensing & Expanding Logarithms Name_____ Date_____ Class____ Condense each expression to a single logarithm. 1) 18loga + 3logb 2) 8logu − 4logv 3) 4logx + 2logy 4) 12lnx + 4lny 5) 2lnx − 5lny 6) lnx + lny + 2lnz Expand each logarithm. 7) log(u5 ⋅ v) 5 8) log(zx⋅y)
This is a 5 part worksheet: Part I Model Problems (with answers explained) Part II Practice Expanding Logarithms; Part III Rewrite Expression as 1 Term; Part IV Extension Problems; Part V Answer Key
Problem 9: Use the rules of logarithms to expand the expression below. Answer [latex]\color{red}3 + {\log _2}\left( 3 \right) + 3{\log _2}\left( {k + 2} \right)[/latex]
