Question

If log 2 =0.3010, log 3 =0.477, log 5 =0.699 = 0.7 then calculate :
(i) ln 2
(ii) ln 6​

Answer 1

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 2

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

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