# Find the value ofn= log 0.2 with base 10/log 0.12 with base 10

2
by sweetysiri92

2014-08-20T11:28:30+05:30
Rule, log(m/n) = log(m) - log(n)

Method (1)
So, log(0.2) = log(2/10) = log(2) - log(10)
As, log(2) base_10 = 0.3010, and log(10) base_10 = 1
So, log(0.2) = 0.3010 - 1 = -0.6990

Method (2)
So, log(0.2) = log(2/10) = log(1/5) = log(1) - log(5)
As, log(1) base_10 = 0, and log(5) base_10 = 0.6990
So, log(0.2) = 0 - 0.6990 = -0.6990

﻿
rule, log(m * n) = log(m) + log(n)
﻿rule, log(m * n * p) = log(m) + log(n) + log(p)

So, log(0.12) = log(12/100) = log(12) - log(100)
﻿Now, log(12) = log(2 * 2 * 3) = log(2) + log(2) + log(3) = 2 * log(2) + log(3)
And log(100) = log(10 * 10) = log(10) + log(10) = 2 * log(10)
As, log(2) base_10 = 0.3010, log(3) base_10 = 0.4771, log(10) base_10 = 1
So, log(12) = 2 * 0.3010 + 0.4771 = 0.6020 + 0.4771 = 1.0791
And, log(100) = 2 * 1 = 2
So, log(0.12) = 1.0791 - 2 = -0.9209
﻿
﻿Thus, log(0.2) / log(0.12) = -0.6990 / -0.9209 = 0.7590

0.7590
2014-08-20T17:07:50+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
N = log 0.2  /  log 0.12        logarithms are with respect to base 10

log 0.2 = log 2 / 10  = log 2 - log 10  = log 2 - 1
log 0.12  = log 12/100 = log 3 * 2² /100 = log 3 + log 2² - log 100
=  log 3 + 2 log 2 - 2

n = log 0.2 / log 0.12
=  [ log 2 - 1 ] / [ log 3 + 2 log 2 - 2 ]