Acquiring logarithmic equations from linear law

It is given that y=axb, where a and b are constants. The diagram below shows the equation by plotting lgy against lg x. Find the value of a and of b.

Solution:

y=axb

lg y = lg(y=axb)

lg y = lg a + b(lg x)

Y = mX + C

m=b, C = lg a

b = (o – (-2)) / (1 -0)              lg a = -2

b = 2                                     a =10-2 

 

                                             a = 1/100

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