If log 2 =0.3010, log 3 =0.477, log 5 =0.699 = 0.7 then calculate :
(i) ln 2
(ii) ln 6
Answers
Step-by-step explanation:
512=2^9
So log(512)to the base 5=log(2^9)/log5
=>9log2/log5
Now we will find the value of log5=log10/2=log10-log2=1–0.301=0.699
(It is very general to use log10=1)
Now we can easily calculate the value of log 512 to the base 5=9(0.301)/(0.699)
=3.8755
Let us use properties of logarithms by converting the given expression to the base 10.
So we have to find
log5512 log5512 so it will equal to log512÷log5 and log 512 = 9(log2) and log 5= log 10 - log 2 or 1-log2
So it will equal to 9×(0.3010)÷(1–0.3010)
Which would be equal to 3.876
Answer:
(i) 0.693
(ii) 1.791
Step-by-step explanation:
lnx = 2.303 * logx
(i) ln2 = 2.303 * 0.301 = 0.693
(ii) ln6 = ln(2*3) = ln2 + ln 3 = 0.693 + 1.098 = 1.791
[ln3 = 2.303 * log3 = 2.303 * 0.477 = 1.098]
Hope it helps
Please mark as brainliest