Question 894424: Without using a calculator how do you solve 5^(123/1000)?
I know this problem can be evaluated as the 1000th root of 5 raised to the 123rd power, so I figured one could solve it using natural logarithms. [I have already found the two formulas for solving an unknown logarithm by hand.] However, when I search for ways to convert (a number (x) raised to a fractional exponent) to a natural log, I can't find any formula that doesn't involve the Euler number (e). All the formulas that have (e) in them also have a fractional exponent to deal with; therefore I'm right back where I started.
So to reiterate, by hand and with NO calculator, how do I convert 5 to the power of (123/1000)to another form that I can solve by using natural logarithms or some other formula or equation?
Thanks.
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Table of Logarithms, as you have found!
You can use natural logs OR common logs (base 10).
You can find good instruction on using common log tables for performing computations from an OLDER intermediate algebra textbook, and the book should be at least 30 years old. Look for any older intermediate algebra book; most of them will have this instruction.
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