Question

For what values of x does 25 Superscript x Baseline = 5 Superscript x squared minus 3?

Answer 1

its

x = –1, x = 3

Explanation:

edge2020

Answer 2

For this case we have the following equation:

`25^(x) = 5^( x^2-3)`

Rewriting we have:

`5^(2 (x)) = 5^( x^ 2-3)\\5^( 2x) = 5^( x^ 2-3)`

For expressions to be equal, exponents must be equal. So:

`2x = x ^ 2-3\\x ^ 2-2x-3 = 0`

To factor, we look for two numbers that, when multiplied, result in -3 and when added, result in -2. These numbers are -3 and 1.

`(x-3) (x + 1) = 0`

Thus, the roots are:

`x_ {1} = 3\\x_ {2} = - 1`

Answer:

`x_ {1} = 3\\x_ {2} = - 1`