If log(base10)of 2 =0.301 and log(base10) of 3 = 0.477, how would I find

Question

a) log(base10) of 8
b) log(base10) of 12
c) log(base10) of 15

Answer 1

(a) log(base10) of 8
log(base10) of 8 can be rewritten as
= log(base10) of (2^3)
= 3*[ log(base10) of 2 ]
= 3*0.301
= 0.903

(b) log(base10) of 12
log(base10) of 12 can be rewritten as
= log(base10) of (2*2*3)
= log(base10) of 2 + log(base10) of 2 + log(base10) of 3
= 0.301 + 0.301 + 0.477
= 1.079

(c) log(base10) of 15
log(base10) of 15 can be rewritten as
= log(base10) of (3*5)
= log(base10) of 3 + log(base10) of 5
= log(base10) of 3 + log(base10) of (10/2)
= 0.477 + log(base10) of 10 - log(base10) of 2
= 0.477 + 1 - 0.301
= 1.176

hope this helps~ :)