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

Question

asked Jan 3, 2021 117k views

2 Answers

Eric Tatara · Answer 1 · 2021-01-08T10:19:29+0000

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:

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