May 2014 Math SL logarithm Help!

[jackrogers121]

Hey guys, would someone please help me out in solving this math problem?

Edited November 15, 2015 by jackrogers121

[steve.muench]

Remember the law of "change of bases" for logarithms, which says:

 

                     log      a

                          c

log    a   =   ____________

      b

                      log     b 

                           c

 

This lets you re-rexpress any log into a new base "c".

 

If you use "a" for "c" here, you get:

 

                     log      a

                          a                               1

log    a   =   ____________  =   ______________

      b

                      log     b                   log   b

                           a                             a

 

 

So, in general if you flip-flop the base and the argument of the log function, you get the reciprocal of what you started with.

 

Try using this idea on the left hand side of the equation in the problem, then find a common denominator to add the two fractions together.

 

Then, a consequence of the Pythagorean theorem will let you further simplify, and then you can do one more round of base/argument flip-flopping to get the final answer.

 

Hope this helps.