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The variables x and y are connected by an equation of the form y= ax^b. when a graph of lg y against lg x is plotted, a gradient of 1.5 and a lgy intercept of 1.2 are obtained. What are values a and b?

Answer 1

Serenity Jones

The given equation #y= ax^b#

Taking #log_10# we get

#log_10y=log_10( ax^b)#

#\>log_10y=log_10 a+blog_10x#

when a graph of #log_10 y# against #log_10 x# is plotted, a gradient #1.5# and intercept 1,2 are obtained. So #b=1.5#

and #" "log_10 a=1.2=>a=10^1.2#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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