What is the common log of 82.5 to 3 significant figures? What is the antilog of

Question

What is the common log of 82.5 to 3 significant figures? What is the antilog of 3.9 to 3 significant figures? The concentration C, in pounds per minute, of one of the components in the outlet stream of a reactor is given by C = log8.56^1.5 lb/min. What is the rate of production of this component? Round up answer to 2 significant figures. Using the relationships between common and natural logs, suppose the number x = 3.3, find the natural and common log using the relationship equation, present your answer in 2 significant figures? What is the anti-natural log of 4.5? Round answer to 2 significant figures

Explanation / Answer

Answer – a) We are given value 82.5 and need to calculate the common log

So, log 82.5 = 1.92.

b) We are given the value 3.9 and need to calculate the antilog

so, antilog 3.9 = 7940

c) We are given the, C = log 8.56 1.5lb/min , we need to calculate the rate of production of this component.

We need to take the log

C = 1.5 lb/min *log 8.56

    = 1.5 l/min * 0.932

    = 1.4 lb/min

So, rate of production of this component is 1.4 lb/min

d) We know the relationship between the common and natural log

we know the common logarithm is the logarithm to base 10

so, natural logarithm, ln = 2.303 * log

ln 3.3 = 1.2

common logarithm 2.303*log 3.3 = 2.303* 0.518

                                                     = 1.2

e) We know the anti-natural logarithm is the inverse function of natural logarithm (ln(x), means it is exponent, so the anti-natural logarithm for 4.5 is

= anti-natural logarithm (4.5)

= 90.

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