1)Solve: (1/5)^(t-2)=125
(1/5)^(t-2)=125
(1/5)^(t-2)=5^3
(1/5)^(t-2)=(1/5)^(-3)
equate the powers on both the sides. we obtain.....
t-2=-3
t=-3+2=-1
t=-1
Jon, you seem to have a pretty good handle on this stuff
I agree with your answers in your last 4 posts.
Thank you.
To solve the equation (1/5)^(t-2) = 125, we can first rewrite 125 as a power of 5. 125 can be written as 5^3.
So, the equation becomes (1/5)^(t-2) = 5^3.
Next, we can rewrite 5^3 as (1/5)^(-3).
Therefore, (1/5)^(t-2) = (1/5)^(-3).
When the bases are the same and the exponents are equal, the equation is true.
So, we can equate the exponents and solve for t.
(t-2) = -3.
Adding 2 to both sides, we get t = -3 + 2 = -1.
Thus, the solution to the equation is t = -1.