2^(3x-5)=1/2^(2x-10) Find x.

Given that: 2^(3x-5) =
1/2^(2x-10)

We will
re-wrtie.

We know from exponent properties that 1/x^a =
x^-a.

==> 1/2^(2x-10) =
2^-(2x-10).

Then, we will
substitute.

==> 2^(3x-5) =
2^-(2x-10)

Now that we have the bases are equal, then the
powers must be equal too.

Then, we conclude that 3x-5 =
-(2x-10)

Let us solve the
equality.

==> 3x - 5 = -2x +
10

We will add 2x to both
sides.

==> 2x+3x - 5 = 2x-2x +
10

==> 5x - 5 = 10

Now
we will add 5 to both sides.

==> 5x - 5 +5 = 10 +
5

==> 5x = 15.

Now we
will divide by 5.

=> x = 15/5 =
3

Then the answer is x =
3