Wells Fargo Logarithms Problems with Solutions Quiz-1

Solution (c). ax = by => log ax = log by => x log a = y log b

=> log a/ log b = y/x

Solution (a). 2 log10 5 + log10 8 – ½ log10 4

= log10 (52) + log10 8 -  log10 (41/2)

= log10 25 + log10 8  - log10 2 = log10 (25*8)/2

= log10 100 = 2

Solution (d). loga (ab) = x => log b/ log a = x => (log a + log b)/ log a = x

1+ (log b/ log a) = x => log b/ log a = x-1

log a/ log b = 1/ (x-1) => 1+ (log a/ log b) = 1 + 1/ (x-1)

(log b/ log b) + (log a/ log b) = x/ (x-1) => (log b + log a)/ log b = x/ (x-1)

=>log (ab)/ log b = x/(x-1) => logb (ab) = x/(x-1)

Solution (a). log8 x + log8 (1/6) = 1/3

=> (log x/ log 8) + (log 1/6 / log 8) = log (81/3) = log 2

=> log x = log 2 – log 1/6 = log (2*6/1)= log 12

Solution (c). Let log9 27 = x. Then, 9x = 27

=> (32)x = 33 => 2x = 3 => x= 3/2

Let log8 32 = y. Then

8y = 32 => (23)y = 25 => 3y = 5 => y=5/3

Solution (d). log12 27 = a => log 27/ log 12 = a

=> log 33 / log (3 * 22) =a

=> 3 log 3 / log 3 + 2 log 2 = a => (log 3 + 2 log 2)/ 3 log 3 = 1/a

=> (log 3/ 3 log 3) + (2 log 2/ 3 log 3) = 1/3

=> (2 log 2)/ (3 log 3) = 1/a – 1/3 = (3-a)/ 3a

=> log 2/ log 3= (3-a)/3a => log 3 = (2a/3-a)log2

log16 16 = log 16/ log 6 = log 24/ log (2*3) = 4 log 2/ (log 2 + log 3)

= 4(3-a)/ (3+a)

Solution(b). log60 3 + log60 4 + log60 5 + log60 (3*4*5)

= log60 60 = 1

Solution (d). log x + log y = log (x+y)

=> log (x+y) = log (xy)

=> x+y = xy => y(x-1) = x

=> y= x/(x-1)

Solution (c). log 27 = 1.431 => log 33 = 1.431

=> 3 log 3= 1.431 => log 3 = 0.477

Therefore, log 9 = log 32 = 2 log 3 = (2*0.477) = 0.954

Solution (c). log 264 = 64 log 2 = (64*0.30103) = 1926592

Its characteristics is 19.

     Hence, the number of digits in 264 is 20