express as a single logorithm and simplify if possible

[synapsis]

log(base a) [3/(sq rt of x)] - log(base a) sq rt 3x

My thinking on this problem is to follow the 2nd logarithm property which says...

log(base b) (u/v) = log(base b) u - log(base b) v

now my weakness with math, and i have been lazy never to seek help, is with dealing with radicals.

following that property i get something like [(3/sq rt x) / (sq rt 3x)]
this, is no where close to the answers i am provided with.

If someone could walk me through this i would be grateful.

 

[stapel]

Hint: Square roots are one-half powers.

Eliz.

 

[synapsis]

Still no help.... my math....

(3/x^1/2)/(3^1/2)

flip the denominator...

(3/x^1/2)*(1/3x^1/2)= 3/3x= 1/x

i'm no where close

 

[tkhunny]

Still no help.... my math....

(3/x^1/2)/(3^1/2)

flip the denominator...

(3/x^1/2)*(1/3x^1/2)= 3/3x= 1/x

i'm no where close

The argument is close

(3/x^1/2)/((3x)^1/2) = 3/[(x^1/2)*(3^1/2)*(x^1/2)]

Where did the logarithm go?

 

[synapsis]

log(base a) 3/1.5x is my final answer?

i'm not going to go into details on the answers provided but i'm using that answer on my paper and I wrote down... is your math correct (to my teacher)

 

[synapsis]

it's not 1.5 it's closer to 1.732 i didn't use () on my calculator

 

[tkhunny]

It's the square root of three.