Answer:
x = 1/10
Step-by-step explanation:
To solve the equation, [tex]2^{2x -1} = 16^{-2x}[/tex] make each base the same. 16 is a multiple 2. The base 16 actually is equivalent to [tex]16 = 2^4[/tex]. Substitute this base and exponent into the equation for 16.
[tex]2^{2x -1} = 16^{-2x}[/tex]
[tex]2^{2x -1} = 2^{4^{-2x}}[/tex]
[tex]2^{2x -1} = 2^{-8x}[/tex]
Now, since each expression is equal and the bases are the same, the exponents must also be equal. Set the exponents equal and solve for x.
2x - 1 = -8x
-1 = -10x
1/10 = x
