Question

express log9 in terms of log3 x and log3 y and solve for x and y simultaneously

Answer 1

let log3 x = a and log3 y = b
then:
3^a = x and 3^b = y
3^a (3^b) = xy
3^(a+b) = xy
(9^(1/2))(a+b) = xy
9^(a+b)/2 = xy

log<sub>9>/sub> xy = (a+b)/2

can you do anything with that?

btw, what does log 9 mean?
is 9 the base, as I assumed ? But then the logarithm had no argument.
Is there a typo?

Answer 2

log3x = a^3 and log3y = b^3
log9xy can be said as ab^9

log3x times log3y is log9xy
log9xy can be expressed as log3x X log3y