grade 12 advanced functions question

Question

solve for x: log₃X - log₃(X-1) = 1

Answer 1

Hi Allan,

 

The most important things to remember about logs are the following

 

y = b^x

is equivalent to

log_b(y) = x

 

AND

 

Subtracting logs with the same base is equivalent to a log of the quotient of those two.  For example.

log₃(x) - log₃(x-1)  = 

           x

log₃ ------   which we know is equal to 1

         x-1

 

Now, using the first "important thing to remember,"

   x

----- = 3¹ = 3

 x-1

 

Now this is reduced to a relatively simple algebraic expression. 

  x
----- = 3
 x-1

 

x = 3(x-1)

x = 3x - 3

3 = 2x

3/2 = x