SOLUTION: Write log a sqrt(6) , in terms of "p" and "q" , if log a 2 = p and log a 3 = q Thank you for taking the time to help me out.

Question 354508: Write log a sqrt(6) , in terms of "p" and "q" , if log a 2 = p and log a 3 = q
Thank you for taking the time to help me out.

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

The first key to this problem is to know that square roots can be expressed using fractional exponents: . So we can rewrite your expression using an exponent of 1/2:

Now we can start using the properties of logarithms:

We can use the third property to remove the exponent:

Now we need to change the argument from a six to something in terms of 2's and/or 3's. It should be obvious that 6 = 2*3 so now we have:

In this form we can use the first property to separate the log into two logs:

Next we can subsitute in for the two logs:

And finally we can use the Distributive Property:

RELATED QUESTIONS
Rewrite the following in terms of p and q where p=log(x) and q=log(y). a)... (answered by stanbon)

Please help me solve this problem: Express log[base b]sqrt((x^2)y), x>0 in terms of p (answered by Theo)

If log base a =p,log base a=q ,express log base a (6) in term of p and q (answered by ikleyn,greenestamps,josgarithmetic)

I'm in need of some help. I have been trying to figure out this question for days but I... (answered by Alan3354)

Given that 'p' equals log16 to the base 'q' (p=logq 16), express in terms of p: logq (answered by nerdybill)

if log 2=p and log 3=q express the following logarithms in terms of p and q 1. log b... (answered by Tatiana_Stebko,lwsshak3)

How do i find the nth term for these sequences? a) log [base 3], log [base 9] 81, log... (answered by Earlsdon)

If log(base 3)2 = P And Log (base 3)13 = Q Express Log(base 78)52 in terms of P and Q (answered by rapaljer)

Question reads: Write in exponential form q=log [37]p (A) 37^p=q (B) 37=p^q (C) (answered by mbarugel)