1. LOGARITHMS exponential logarithmicm b Alogb ( A)m b>0 A>0Jeff Bivin -- LZHS

2. exponentiallogarithmic m b Alogb ( A)m 2 3 9 log3 (9)2 53 125log5 (125)3 3 1 1 2 8log2 8 3 1 5 2 32 log1 (32) 52 y x 2 log2 ( x)yJeff Bivin -- LZHS 3. Evaluate log5 (25)u u 525u 25 5 u2 log5 (25)2Jeff Bivin -- LZHS 4. Evaluate log3 (81) u u 3 81 u 4 3 3u4 log3 (81) 4Jeff Bivin -- LZHS 5. Evaluate1log232uu1232u12252u 25u 51 log232 5Jeff Bivin -- LZHS 6. Try this!! log7 (7) u u 77 u1 77u 1 log7 (7) 1Jeff Bivin -- LZHS 7. Try this!!Solve for x logx(32) = 5x5 = 32x5 = 25 x = 2Jeff Bivin -- LZHS 8. Try this!!loga (1)? 0a1 loga (1)0Jeff Bivin -- LZHS 9. Try this!!loga (a)? 1aa loga (a)1Jeff Bivin -- LZHS 10. Special Logarithmslog10 a log aloge aln a 11. Properties of Logarithms Product Property Quotient Property Power PropertyJeff Bivin -- LZHS 12. Product Propertym n m na a a multiplication additionlogb (m n)logb (m)logb (n)multiplicationadditionJeff Bivin -- LZHS 13. Product Property log2 (16 4) log2 (16) log2 (4)4 24 2log2 (2 2 )log2 (2 ) log2 (2 )6 log2 (2 ) 4 266Jeff Bivin -- LZHS 14. Quotient Property m a m ndivision n a subtraction a mlog ( )b nlogb (m) logb (n) divisionsubtractionJeff Bivin -- LZHS 15. Quotient Property32 log2 4log2 (32) log2 (4) 5 2log2 8 log2 (2 ) log2 (2 )3 log2 (2 ) 5 2 3 3Jeff Bivin -- LZHS 16. Power Propertym n mna ap logb(m p ) logb(mp ) = plogb(m)Jeff Bivin -- LZHS 17. Power Property7 log2 2 7 log2 (2)7 717 7Jeff Bivin -- LZHS 18. Power Property n log a an n.log a ( a )n.1nJeff Bivin -- LZHS 19. Change of Base Formula logb x loga x logb alog x log a xlog aJeff Bivin -- LZHS 20. log b 1 1log a b log alog alogb a log b log b log c log c log a b.logb c . log a c log a log b log a n n log b n.log bn log am bm.log a b log a m.log amJeff Bivin -- LZHS 21. Expand 3 2 log5 ( x y )3 2product propertylog5 ( x )log5 ( y )power property 3 log5 ( x)2 log5 ( y)Jeff Bivin -- LZHS 22. Expand x7 log 5 y2 z5 7 2 5quotient property log5 ( x ) log5 ( y z )product propertylog5 ( x )72 log5 ( y )5log5 ( z )distributive property log5 ( x )7 2 log5 ( y )5 log5 ( z )power property7 log5 ( x)2 log5 ( y)5 log5 ( z)Jeff Bivin -- LZHS 23. Condense 5 log3 x 6 log3 y2 log3 zpower propertylog3 x 5 log3 y 6log3 z 2product property log3 x y 56log3 z 2 x5 y 6quotient propertylog 3z2Jeff Bivin -- LZHS 24. Condense 1 2 log10 x2 log10 y 4 log10 z 124Power property log10 x 2 log10 ylog10 z 124group / factor log10 x 2log10 y log10 z1product property 2 4 log10 x2log10 y z1quotient property log10x2logx y2z4 10 y 2 z 4Jeff Bivin -- LZHS 25. Logarithm EquationsPropertieslog a B log a C B CJeff Bivin -- LZHS 26. Solve for x log3 3x9 log3 x 3 3x 9 x32x12x 6Jeff Bivin -- LZHS 27. Solve for x log3 3x 9 log3 x3check x 6 log3 3(6) 9log3 6 3log3 189log3 6 3 log3 9 log3 9 checks!Jeff Bivin -- LZHS 28. Solve for x log3 3x9 log3 x 3 3x 9 x32x12x 66Jeff Bivin -- LZHS 29. Solve for x log4 7 log4 n 2 log4 6nlog4 7(n 2)log4 6n7n14 6nn14Jeff Bivin -- LZHS 30. Solve for x log4 7 log4 n 2 log4 6ncheckn 14 log4 7 log4 142 log4 6(14) log4 7log4 12log4 84log4 7(12)log4 84 log4 84log4 84 checks!Jeff Bivin -- LZHS 31. Solve for x log4 7 log4 n 2 log4 6nlog4 7(n 2)log4 6n7n14 6nn1414Jeff Bivin -- LZHS 32. Solve for x log2 x 1log2 x 133 log 2 ( x 1)( x 1) log 2 2 3 ( x 1)( x 1)2 2 x 1 8 2 x 9 x 3Jeff Bivin -- LZHS 33. Solve for x log2 x 1 log2 x 1 3 check x 3 check x3 log2 3 1log2 3 1 3 log23 1log2 3 1 3log2 4 log2 2 3log22 log2 4 3 2 13fails 33 The argumentchecks! must be positiveJeff Bivin -- LZHS 34. Solve for x log2 x 1 log2 x 13log2 ( x 1)(x 1)332 ( x 1)(x 1)28 x 129 x3 x3Jeff Bivin -- LZHS 35. xx 33 27 3 3x 3xx 25 49 5 7 ???????? 36. Solve exponential equation withlogarithmsx x 2549 5 7???????? log 5 xlog 7 2 x.log 52.log 7 log 7x 2. log 5x 2.log 5 7 37. Solve for x4x 2 log 5 log 7 (4 x) log(5) (2) log(7)4 log(5) 4 log(5) 2 log( 7 ) x 4 log(5 ) log(7 2 ) x log(54 )xlog 625 (49)Jeff Bivin -- LZHS 38. Solve for x x 2x 1log 3log 5 ( x 2) log(3) ( x 1) log(5) x log(3) 2 log(3) x log(5) 1log(5) x log(3) x log(5) log(5) 2 log(3)x log(3) log(5)log(5) 2 log(3)5log( ) 5 x93 xlog 3 ( )log( ) ( ) 95 5Jeff Bivin -- LZHS 39. Try this3x 157 253x 1 log7 log 25log(7 ) (3x 1) log(2)5 log( 7 ) 3x log(2) 1 log(2)5log(7 )log(2) 3x log(2) log( 10 ) log(8) 7x 10log ( )Jeff Bivin -- LZHS 8 7x 40. Try this 3x 2 ln 15ln e ln(15)1(3x 2) ln(e) ln(15) 3x 2 ln(15) 2 3x ln(15) 2 3xJeff Bivin -- LZHS