Show that `1/(log6 a) + 1/(log4 a) = 1/(log24 a)`

Expert Answers
tiburtius eNotes educator| Certified Educator

We will use formula for change of base:


So we have:

`1/(log_6 a)+1/(log_4 a)=1/((log_(24) a)/(log_(24) 6))+1/((log_(24)a)/(log_(24) 4))=(log_24 6)/(log_24 a)+(log_24 4)/(log_24 a)=(log_24 6+log_24 4)/(log_24 a)`

Now we use formula for logarithm of product:

`log_b(xy)=log_b x+log_b y`

So our expression is equal to:

`(log_24(6cdot4))/(log_24 a)=(log_24 24)/(log_24 a)=1/(log_24 a)`

For more on logarithms see the ling below.