I keep getting questions like $4^.6$, and likewise - since nothing online has helped I've reverted to remembering, which is not very good.
So, is there a way to calculate this with a formula?
The only logical way I can think of is: Take $4^.6$, for example. In this equation it would be $4*(4*0.6)$. With my formula, I get $9.6$; but the real answer is $2.29739671$.
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Plqsmic
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Why do you remember them? Use the calculator. – Math Lover Nov 16 '17 at 01:50
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1Are you asking about calculating square roots or powers of $0.6$? Your post is not clear at all. – Deepak Nov 16 '17 at 01:51
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@MathLover how would I put it in the calculator? – Plqsmic Nov 16 '17 at 01:52
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$x=4^.6 \Rightarrow lnx=.6 ; ln4 \Rightarrow x=e^{.6;ln4}$. Approximate $e^{.6;ln4}$ (e.g. with McLaurin series) and here you go! With a scientific calculator it is $exp(0.6*log(4))$ – cyanide Nov 16 '17 at 01:53
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Then, the question would be how to approximate $\ln(4)$. (Of course, there is an effective way to do that, but I think this is not what the OP is aiming for.) – Batominovski Nov 16 '17 at 01:54
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@BlazeDaBlur Most calculators have a button for $x^y$. – Math Lover Nov 16 '17 at 01:54
2 Answers
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$e^{.6∗ln(4)}$
or
$exp(0.6∗log(4))$
Any scientific calculator must have $log$ and $exp$ functions.
See comments above.
cyanide
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$$x^{ab}=(x^a)^b$$ holds for every real number $x$. So to calculate $x^{0.6}$ you can use $(x^6)^{1/10}=\sqrt[10]{x^6}$.
Stella Biderman
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