Question

Solve: 12^x2+5x-4 =12^2x+6

Answer 1

C) x = 2, x = -5

Explanation:

took quiz

Answer 2

x=2, x=-5

Explanation:

to work more comfortably, the first thing we need to do is work the equation linearly, for that we take advantage of the property of logarithms that tells me that
`log(a^(b))=b*log(a)`

in this way, the equation remains as:

`log(12^{x^(2) +5x-4 } )=log(12^(5x+6) ) \\ (x^(2) +5x-4 )*log(12)=(5x+6) *log(12)\\x^(2) +5x-4 = 5x+6`

Now we clear the equation so that it is of the form
`ax^(2) +bx+c=0`

`x^(2) +5x-2x=6+4\\ x^(2) +3x-10=0`

finally, we apply the equation to solve second degree equations

`x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}`

`x = \frac{-3 \pm \sqrt {3^2-4*1*(-10)}}{2*1}\\ x = \frac{-3 \pm \sqrt {9+40}}{2}\\ x = (-3 \pm 7)/(2)`

x=2 and x=-5

Done