SOLUTION: The sides of a triangle have lengths log(base 2)3, log( base 2)7,and log(base 2) x. Find the least possible integral value of x?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The sides of a triangle have lengths log(base 2)3, log( base 2)7,and log(base 2) x. Find the least possible integral value of x?       Log On


   

Question 526775: The sides of a triangle have lengths log(base 2)3, log( base 2)7,and log(base 2) x. Find the least possible integral value of x?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The length of the third side of a triangle must be less than the sum of the length of the other two sides, and more than the difference. If you imagine playing with the angle the two sides make, you would see that as you make the angle measure smaller the length of the third side becomes smaller. When the measure of the angle is 0 degrees, the length of the third side is the difference of the lengths of the other two sides, but you do not have a triangle any more.
log%282%2C7%29-log%282%2C3%29%3Clog%282%2Cx%29
If you know about logarithms, you would know that
log%282%2C7%29-log%282%2C3%29=log%282%2C7%2F3%29 and that
log%282%2C7%2F3%29%3Clog%282%2Cx%29 means that 7%2F3%3Cx
So you are looking for the smallest integer that is more than 7%2F3