How to calculate the value of b if the equation is 1/T^2=1/T^b?

Indranil

Junior Member
How to calculate the value of b, if the equation is 1/T^2=1/T^b?

Dr.Peterson

Elite Member
How to calculate the value of b, if the equation is 1/T^2=1/T^b?
There is an obvious solution; do you see it?

But were you told the value of T, or what its possible values are? (If T were 1, everything would change!)

Jomo

Elite Member
How to calculate the value of b, if the equation is 1/T^2=1/T^b?
What have you tried? where are you stuck? It is hard to help you if you do not tell us where you are stuck.

I'll try to start you off. On both sides of the equal sign you are dividing 1 by different expressions (T^2 and T^b). What do you think must be true of the two expressions (are their sum 17, is their difference 11, are they equal to one another....?)

HallsofIvy

Elite Member
Do you see that if 1/x= 1/y then x= y? If that not obvious multiply both sides of 1/x= 1/y by xy.

Indranil

Junior Member
What have you tried? where are you stuck? It is hard to help you if you do not tell us where you are stuck.

I'll try to start you off. On both sides of the equal sign you are dividing 1 by different expressions (T^2 and T^b). What do you think must be true of the two expressions (are their sum 17, is their difference 11, are they equal to one another....?)
Do you mean to say
1/T^2 = 1/T^b
or, T^b = T^2
or, b = 2

Last edited:

Indranil

Junior Member
Do you see that if 1/x= 1/y then x= y? If that not obvious multiply both sides of 1/x= 1/y by xy.
1/x X xy = 1/y X xy

or, y = x, still I don't understand how to find the value of b if the equation is 1/T^2 = 1/T^b

HallsofIvy

Elite Member
Do you mean to say
1/T^2 = 1/T^b
or, T^b = T^2
or, b = 2
Yes, that is correct.

HallsofIvy

Elite Member
1/x X xy = 1/y X xy

or, y = x, still I don't understand how to find the value of b if the equation is 1/T^2 = 1/T^b
In your example, x= T^2 and y= T^b. so (1/T^2)(T^2T^b)= (1/T^b)(T^2T^b) which give T^b= T^2.

As you saw in your previous post that gives b= 2.

Jomo

Elite Member
Do you mean to say
1/T^2 = 1/T^b
or, T^b = T^2
or, b = 2
If you erased the b in your problem what would you replace it with so both sides look exactly the same. The answer is 2, so yes b = 2.

Thank you all.