SOLUTION: Please help with the following question, I'm about ready to yank my hair out... Let {{{ log (b, 2) }}} equal A and {{{ log (b, 3) }}} equal C. Write the expression below in term

I think you just didn't remember that the square root is the same
as the  power.

 

We observe that 32 = 2*16 = 2*2*8 = 2*2*2*4 = 2*2*2*2*2 = 25
We observe that 27 = 3*9 = 3*3*3 = 33



We observe that the square root is the  power:



Now we use a rule of logarithms that allows us to move the 
exponent in front as a coefficient of the log:



Now we can write the log of a quotient as the difference of the logs,
being careful to place the difference of logs in parentheses so that
the  is multiplied by both terms:



Now on each of those terms inside the parentheses, we again use the
rule of logarithms that allows us to move the 5 and 2 exponents in 
front as a coefficient of the logs:



Finally we substuitute A for  and C for 



Yoou can leave it like that or write it over 2 like this:



or as



or as



Edwin