Give a counterexample to the claim log (s/t) = log s/ log t

Question

Give a counterexample to the claim log (s/t) = log s/ log t

Answer 1

Let s = 100 and t = 10

log(s)=2,  log(t)=1

log(s/t)=1 log(s)/log(t)=2

Answer 2

"Give a Counterexample" just means find any substitutes for s and t that prove the equation is wrong. 

 

Okay, we know that the log of 1 is zero, right?  So, let's pick s=t, so s/t = 1 and the left of the equation has a value of zero.

 

But, the only way that the right half of the equation can equal zero, is if the top half of the fraction, log(s), is zero, right?  And literally, any S (other than 1) will give an answer that isn't zero on the right side of the equal sign. 

 

If s=t=5, for example, then the left side goes to zero and the right side goes to 1, proving the equation is wrong.