SOLUTION: Let r = log16 4, s = log16 11, t = log4 11.Rewrite the expression below in a form with no logarithm of a product, quotient or power. Then use some, or all, of the letters r, s, t t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Let r = log16 4, s = log16 11, t = log4 11.Rewrite the expression below in a form with no logarithm of a product, quotient or power. Then use some, or all, of the letters r, s, t t      Log On


   

Question 1121935: Let r = log16 4, s = log16 11, t = log4 11.Rewrite the expression below in a form with no logarithm of a product, quotient or power. Then use some, or all, of the letters r, s, t to enter this new form of the logarithm in the answer blank.
log(base16)(4squareroot(11))= ?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Given:
log%2816%2C4%29+=+r
log%2816%2C11%29+=+s
log%284%2C11%29+=+t

To find:
log%2816%2C%284%2Asqrt%2811%29%29%29

Using basic logarithm rules,



So one form of the answer, according to the given rules, is

r + s/2

There are many other forms for the answer.

Note that t = 2s; so another form of the answer could be

r+t/4

And note further that r is just 1/2; so other forms of the answer are

1/2+t/4

or

1/2+s/2

or

(1+s)/2