Question

Solve the equation 2 to the power 2 x - 1 = 16 to the power -2x​

Answer 1

x = 1/10

Explanation:

To solve the equation,
`2^(2x -1) = 16^(-2x)` make each base the same. 16 is a multiple 2. The base 16 actually is equivalent to
`16 = 2^4`. Substitute this base and exponent into the equation for 16.

`2^(2x -1) = 16^(-2x)`

`2^(2x -1) = 2^{4^(-2x)}`

`2^(2x -1) = 2^(-8x)`

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