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.

 

[CellCoree]

Solving for an exponent that is pi and a cube root can be done by first understanding the properties of exponents and roots.

An exponent represents the number of times a number is multiplied by itself, while a root represents the inverse operation of an exponent.

To solve for an exponent that is pi and a cube root, we can first rewrite the expression as (pi)^1/3. This means we are taking the cube root of pi raised to the first power.

To solve this, we can use a calculator or manually calculate the cube root of pi. The approximate value of pi is 3.14159, so the cube root of pi would be approximately 1.464.

In general, when solving for an exponent that is a non-integer value, we can use logarithms or a calculator to find the value.

For example, if the exponent was 2.5, we could use the logarithm function to find the value of 2.5^x = pi.

As for solving when an exponent is pi, we can also use logarithms or a calculator to find the value. We can rewrite the expression as pi^x = a, where a is the number we are trying to solve for.

Using logarithms, we can take the natural log of both sides to get xln(pi) = ln(a). We can then solve for x by dividing both sides by ln(pi).

In general, when solving for an exponent that is a non-integer value, we can use logarithms to find the value.

I hope this helps and clarifies the process for solving for an exponent that is pi and a cube root. Don't worry about being slow, math can be complex and it's important to take the time to fully understand the concepts. Keep practicing and asking questions, and you'll continue to improve your mathematical skills.