Question

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

Answer 1

Answer:

x=2, x=-5

Step-by-step 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

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

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

x=2 and x=-5

Done