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 can be converted to the base b by the formula .

Problem 2: Find .

Answer: 0.43068

Solution 1: Convert to the base 10.

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 , then the answer is correct.

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 to the base e.

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

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