SOLUTION: Show every step. This is a proof. If {{{log_b(x)=(1/2)log_b(v+3)}}}, show that {{{x = (b^3) sqrt(v)}}}

Algebra ->  Proofs -> SOLUTION: Show every step. This is a proof. If {{{log_b(x)=(1/2)log_b(v+3)}}}, show that {{{x = (b^3) sqrt(v)}}}      Log On


   

Question 1129935: Show every step. This is a proof.
If log_b%28x%29=%281%2F2%29log_b%28v%2B3%29, show that x+=+%28b%5E3%29+sqrt%28v%29
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The statement is not true; so it can't be proved.

Use "nice" numbers to find a counterexample: b=2, v=13. Then the right side of the given equation evaluates to

%281%2F2%29log_2%2813%2B3%29+=+%281%2F2%29log_2%2816%29+=+%281%2F2%29%284%29+=+2

Then the equation says the expression on the left, log_2(x), is equal to 2. So

log_2(x)=2 --> x = 2^2 = 4.

But the statement we are trying to prove is x = (b^3)^sqrt(v), and it is certainly not true that

4 = (2^3)(sqrt(13).

Note that if you show the given equation correctly, a proof is possible....