Expert: Steve Holleran - 7/18/2008

Question
25^-2x=5^6x-3 as well as log4(5x-1)=3

Answer
Hi Joey,

On the first equation, you want to write each side as a power of a common base number.  In this case, you want to use 5, because the right side has 5 as the base, and 25 is a power of 5:  25 = 5^2.

So, it goes like this:

                          25^(-2x) = 5^(6x-3)

                          [5^2]^(-2x) = 5^(6x-3)

                          5^(-4x) = 5^(6x-3)

                 
Now, if these are equal, the powers must be equal:

                            -4x = 6x-3

                            10x = 3    so                 x = 3/10.


For the second one, change it to an exponential equation:

          log4(5x-1) = 3--------------> 4^3 = 5x-1

                                        64 = 5x-1

                                        65 = 5x   so x = 13.


Hope this helps,
Steve