If log 2=0.3010,log 3=0.4771 and log 5=0.6990 find log 12.5–log6.25

Answer 1

First, let's find log 12.5. We can rewrite 12.5 as 25/2 to make the calculation easier. Using the logarithm property log (a/b) = log a - log b, we have:

log 12.5 = log (25/2)
= log 25 - log 2
= 2 log 5 - log 2
= 2(0.6990) - 0.3010
= 1.3980 - 0.3010
= 1.0970

Next, let's find log 6.25. We can rewrite 6.25 as 25/4 to make the calculation easier. Using the logarithm property log (a/b) = log a - log b, we have:

log 6.25 = log (25/4)
= log 25 - log 4
= 2 log 5 - 2 log 2
= 2(0.6990) - 2(0.3010)
= 1.3980 - 0.6020
= 0.7960

Finally, let's find log 12.5 – log 6.25:

log 12.5 – log 6.25 = 1.0970 - 0.7960
= 0.3010

Therefore, log 12.5 – log 6.25 = 0.3010