Question

Given log4 = 0.60206. log3 = 0.4771213. Find the logarithms of (1) 0.8 (ii) 0.003 (1) 0.108 (1) (0.0008)​

Answer 1

Answer:

log 4 = 0.60206

or, log$2^{2}$ = 0.60206

or, 2log2 = 0.60206

or, log 2 = 0.30102

Also, log 10 = 1

1) Log 0.8 = log (8 x $10^{-1}$)  = log 8 + log $10^{-1}$ = log$2^{3}$ + log $10^{-1}$

                = 3log2 - 1 = 3(0.30102) - 1 = 0.90306 - 1 = - 0.09694

2) log 0.003 = log(3 x $10^{-3}$) = log 3 + log $10^{-3}$  

                     = log 3 - 3 = 0.4771213 - 3 = -2.5228787

3) log 0.108 = log 108 X $10^{-3}$ = log108 + log $10^{-3}$  = log($2^{2}$ + $3^{3}$) + log $10^{-3}$

      = 2log2 + 3log3 - 3

     = 0.60206 + 1.4313639 - 3 = -0.9665761

4) log 0.0008 = log(8 x $10^{-4}$) = 3log2 - 4 = 0.90306 - 4 = -3.09694