Applications of Logarithms

[eutas1]

Hello, I am stuck on this question - please refer to the attachment.

Are you allowed to just get rid of the t^2 + 1 (by multiplying to the other side, which equals 0) ??? I remember my maths teacher telling me you cannot get rid of an unknown variable (in this case, that would be 't') when calculating f'(x) = 0. So how come it does that in the worked solution?

 

[LCKurtz]

[imath]t^2+1\ne 0[/imath] so you don't have a zero in the denominator in the first place. The only way a fraction can be 0 is if the numerator is 0. It is OK to multiply both sides of an equation by a non zero quantity. It isn't the same thing as having something like [imath]t^2-2t=0[/imath] and dividing both sides by t, which would cause you to lose the root [imath]t=0[/imath].

 

[eutas1]

[imath]t^2+1\ne 0[/imath] so you don't have a zero in the denominator in the first place. The only way a fraction can be 0 is if the numerator is 0. It is OK to multiply both sides of an equation by a non zero quantity. It isn't the same thing as having something like [imath]t^2-2t=0[/imath] and dividing both sides by t, which would cause you to lose the root [imath]t=0[/imath].

Ah! I see, thank you!

 

[Steven G]

Yes, it is true that the only way a fraction can be 0 is if the numerators 0, but that is not sufficient. A fraction equals 0 if and only if the numerator is 0 and the denominator is not 0. 0/0 is not 0.