3 x square root of 27 = 3^n

Question

3 x square root of 27 = 3^n 

Find the value of n.

 

Please explain how to answer this question. Thank you :)

 

P.S. How do you insert a square root symbol (so as to make asking questions like this easier)? 

Answer 1

Tahlia,

 

You can represent square root in various ways:  √27  =  (27)^1/2  =  (27)^0.5.  The √ symbol can be found by clicking the Ω symbol above.

 

Now to your problem:  3ⁿ = 3 √27  = 3 √(9)(3)  = (3)2 √3  = (3) ^(5/2).

So n = 5/2

 

You can also solve it by taking natural logs of both sides and working both sides to get n = 5/2.