Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 345

Method for; 3^c=1/ √3 ?

Third and final part of the question.

Again, I could work it out, but I’m looking for the proper method.

Trial and error;
1 over suggests a reciprocal, maybe, so a negative 1 might be involved…
Fraction for answer might imply a fractional index…
√3 would mean 2 for the denominator

Try 3^-1/2
= (√3)^-1
= 1/√3

So c=-1/2

---

Prioritise. Persevere. No pain, no gain.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 256

Re: Method for; 3^c=1/ √3 ?

3^c = 1 / √3
3^c = 1 / 3^(1/2)
3^c = 3^(-1/2)

c = -1/2

Last edited by KerimF (2023-12-17 14:25:51)

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Method for; 3^c=1/ √3 ?

I’m looking for the proper method...for 3^c=1/ √3 ?

Remember that sqrt is 1/2 power & flipping is minus
1/sqrt{3}=1/(3^(1/2))=3^{-(1/2)}
so c=-1/2
Always try to convert sides to same base
Then set powers equal and solve - no guessing

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Method for; 3^c=1/ √3 ?

3^c = 1 / √3
3^c = 1 / 3^(1/2)
3^c = 3^(-1/2)

c = -1/2

Thanks, KerimF, you've been really helpful.

---

Prioritise. Persevere. No pain, no gain.

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Method for; 3^c=1/ √3 ?

I’m looking for the proper method...for 3^c=1/ √3 ?

Remember that sqrt is 1/2 power & flipping is minus
1/sqrt{3}=1/(3^(1/2))=3^{-(1/2)}
so c=-1/2
Always try to convert sides to same base
Then set powers equal and solve - no guessing

Thanks, amnkb

---

Prioritise. Persevere. No pain, no gain.