Use properties of logarithms to expand the logarthmic expression as much as poss

Question

Use properties of logarithms to expand the logarthmic expression as much as possible Where possible, evaluate logarthmic expressions without using a calculator. log (100z) 100 Prevew My Answers Stoma Answers Show me another Secure https/Aww1 math msu edia/webwork2 point) Use properties of logarthms to expand the kogarthmic expression as much as possible where possible evaluate logarthmic expressions wnhout using a calculator Use properties or logarinms to expand the logarthmic expression as much as possible Where possible, evaluate logartmmic expressions without using a calculator Or +7013 103 ss 17.75720 O This problem has several parts which are revealed sequentially after the preceding part has been answered correctly. In this exerdie you wil expand the given logarthmic expression one step at a time logs logs

Explanation / Answer

log (100x) = log(100)+log x= log(102)+ log x = 2+log x ( as log mn= log m +log n). ln( e6/8) = ln (e6) –ln 8 = 6ln e – ln 8 = 6- ln 8 ( as log mn = n log m and ln e = 1) ln[x4 (x2+6)/(x+7)13]=ln[x4(x2+6)1/2/(x+7)13]=ln[x4(x2+6)1/2]-ln(x+7)13=ln (x4) + ln(x2+6)1/2 - ln(x+7)13 = 4 ln x + (½)ln(x2+6)- 13 ln(x+7) ( as log m/n = log m –log n) logb (x6 y/z9) = logb (x6y)- logb(z9)=logb(x6) + logb ( y)- logb(z9) = 6 logb x +(1/2) logb y -9 logb z. log2 56 –log2 7 = log2(56/7) = log2(8) = log2 (23) = 3. 8 ln(x+19) -6 ln x= ln(x+19)8 –ln x6 = ln [(x+19)8/x6]. 1/6(log4 x-log4y)+9log4(x-3)= (1/6)log4(x/y)+log4(x-3)9=log4(x/y)1/6+log4(x-3)9=log4[x1/6(x-3)9/y1/6] log x +log (x2-49)-log 12-log (x+7) = log x +log [(x+7)(x-7)]- [log 12+log (x+7)] = log[x(x+7)(x-7)]- log (12*(x+7)]= log[x(x+7)(x-7)/ 12*(x+7)] =log [ x(x-7)/12].

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