CHANGING THE BASE OF A LOGARITHM - Problem 2

Let a, b, and x be positive real numbers such that neither a nor b equals 1 (remember x must be greater than 0). Then tex2html_wrap_inline48 can be converted to the base b by the formula tex2html_wrap_inline50 .

Problem 2: Find tex2html_wrap_inline52 .

Answer: 0.43068

Solution 1: Convert tex2html_wrap_inline52 to the base 10.

displaymath56

rounded to 0.43068. If you use continuous calculation on your calculator, your answer will be 0.4306766.

Check: Let's check your answer. If tex2html_wrap_inline58 , then the answer is correct.

tex2html_wrap_inline58 is not exact but close enough for our check. Remember why it is not exact in the check. the value of log4 and log25 were rounded, divided, and the answer rounded again.; therefore, the answer won't be exact. If you use continuous calculation and memory on your calculator, the answer will be even closer.

Solution 2: Convert tex2html_wrap_inline52 to the base e.

displaymath64

If you used continuous calculation and memory in your computer, your answer would be 0.4306766

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Author: Nancy Marcus

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