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Calculus IChapter 1: ReviewSection 1-8

Logarithm Functions — Question 8

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Question 8

Let f(x)=log⁡bxf(x)=\log_b x, where b>0b>0 and b≠1b\ne1. Suppose that f(2)=1andf(5)≈2.32193.f(2)=1\qquad\text{and}\qquad f(5)\approx2.32193.

  • (a) Estimate f(10)f(10) using logarithm properties.

  • (b) Estimate f(5/2)f(5/2) using logarithm properties.

  • (c) Explain the properties used.

Original worksheet page 1: question and worked solution for 1-8-008
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Question 8 - Solution

The product and quotient laws hold for positive arguments:

f(10)=f(2)+f(5)≈1+2.32193=3.32193,f(10)=f(2)+f(5)\approx1+2.32193=\boxed{3.32193},

f(5/2)=f(5)−f(2)≈2.32193−1=1.32193.f(5/2)=f(5)-f(2)\approx2.32193-1=\boxed{1.32193}.

The datum log⁡b2=1\log_b2=1 fixes b=2b=2, so the supplied approximation to log⁡b5\log_b5 is consistent with the same base.

Original worksheet page 2: question and worked solution for 1-8-008

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