Question

Write each of the following expressions as log N. Determine the value N. (you can assume the base is 10, but the result are identical which ever base is
used)


1)log 16 - log 2

2) 3 log 4

3) 2 log 3 - 3 log 2

4) log 243 + log 1

5) log 10 + 2 log 3 - log 2

Answer 1

1)log 16 - log 2   =  log (16/2)   =  log 8    Here N = 8

2) 3 log 4  = log 4³  = log 64    Here N = 64

3) 2 log 3 - 3 log 2  =  log 3² - log 2³ = log 9 - log 8  = log (9/8) ..Here N = 9/8

4) log 243 + log 1 = log (243*1) = log 243    Here N = 243

5) log 10 + 2 log 3 - log 2  = log 10 + log 3² - log 2  
 = log 10 + log 9 - log 2  =  log (10*9) - log 2   = log 90 - log 2  = log (90/2) = log 45....Here N = 45

Answer 2

(1)log 16 - log 2   =  log (16/2)   =  log 8    so  N = 8(log m-log n=log m/n

(2) 3 log 4  = log 4³  = so N = 64(mlogn=logn^m)

(3) 2 log 3 - 3 log 2  =  log 3² - log 2³ = log 9 - log 8  = log (9/8) so = 9/8(law mentioned above

(4) log 243 + log 1 = log (243*1) = log 243    so N = 243(log m+log n=log mn)

(5) log 10 + 2 log 3 - log 2  =  = log 10 + log 9 - log 2  =  log (10*9) - log 2   = log 90 - log 2  = = log 45 so  N = 45(log m-log n=log m/n)
these laws are applicable only to briugs logarithms where base is 10