logarithm question, PLEASE HELP, i'd appreciate it!?

log9 27 * log2 8

= log(3^3)/log(3^2) * log(2^3)/log(2)

= 3log(3)/2log(3) * 3log(2)/log2

= 3/2 * 3 = 9/2

(property :-- log a N =z so N=a^z)

log9 27=x

27=9^x (using the above property)

3^3=3^2x

as the base are same i.e=3 so equating the powers

3=2x

x=3/2

log2 8=y

8=2^y (again using the property)

2^3=2^y

again base is same i.e 2 so equating the powers

y=3

log9 27 . log2 8=x*y=3/2*3=9/2

A scientific calculator can tell you that log (base 9) of 27 is 1.5.

But if you remember that 3^2 = 9 and 3^3 = 27, then you can figure out the answer in your head:

3/2 = 1.5

The final answer to your question is 1.5 * 3 = 4.5

log9 27 is the solution of 9^x=27

9=3^2 and 27=3^3

so we get

(3^2)^x=3^3

that is

3^(2x)=3^3

hence 2x=3

and x=1.5

log9 27 = 1.5

log_9 (27) = log_9 (9^3/2) = 3/2