SOLUTION: Write as a single logarithm 2+(1/2)log5(x-1)-3log5(2z)+(2/3)log5(y)-log5(a)

The first term " 2 " must be written as a logarithm with base 5.  
Here is how to do that:

Let N be such that log5(N) = 2

Then by the definition of lagarithm, 52 = N,

so we write 2 as log5(52) 

Now we have:

 

We move all coefficients of logs as exponents of whatever the log is
being taken of:


 

Write all the terms that have " + " before them together and those
that have " - " before them together:

  

Group the terms with + and group those with - preceded by a minus sign:



Inside both parentheses, use the rule of logs that says
"the sum of logs is the log of the product"



Finally, use the rule of logs that says
"the difference of two logs is the log of the quotient (division)



You can finish by :

1. writing 25 as 25.
2. writing (2z)3 as 23z3 and again as 8z3



Edwin