MHB How do you solve for an exponent that is pi and a cube root?

[OMGMathPLS]

How do you solve when an exponent is pi?

And a cube root.

Thanks, sorry I'm slow.View attachment 3285

 

[topsquark]

How do you solve when an exponent is pi?

And a cube root.

Thanks, sorry I'm slow.View attachment 3285

Once in a while you will have a "perfect" cube root, ala the cube root of 27, but in general you have to use a calculator.

-Dan

 

[chisigma]

How do you solve when an exponent is pi?

And a cube root.

Thanks, sorry I'm slow.View attachment 3285

In general for a > 0 the following identity holds...

$\displaystyle a^{b} = e^{b\ \ln a}\ (1) $

... so that the six numbers are $\displaystyle e^{\ln 4.2},\ e^{\pi\ \ln 2},\ e^{\frac{1}{2} \ln 15},\ e^{2.5\ \ln 2},\ e^{\frac{1}{3}\ \ln 73},\ e^{3\ \ln \pi}$, and at this point You have to work on the exponents...

Kind regards

$\chi$ $\sigma$

 

[OMGMathPLS]

Thanks. I will put it in a calculator.