Question

What’s the answer to this question below. A b c or d

Answer 1

Choice C is the correct answer.

Explanation:

We have given that

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

We have to find the values of x.

Same base have equal powers.

x²+5x-4 = 2x+6

Adding -2x-6 to both sides of above equation, we have

x²+5x-4-2x-6 = 2x+6-2x-6

x²+3x-10 = 0

Splitting the middle term of above equation, we have

x²+5x-2x-10 = 0

Making groups, we have

x(x+5)-2(x+5)= 0

Taking common ,we have

(x+5)(x-2)= 0

Applying Zero-Product Property , we have

x+5 = 0 or x-2 = 0

x = -5 or x = 2

Choice C is the correct answer.

Answer 2

option C

x = 2 , x = -5

Explanation:

You have to remember the "Quotient Rule" for exponent having same base.

The quotient rule tells us that we can divide two powers with the same base by subtracting the exponents.

Here,

base = 12

exponents = (x² + 5x - 4) , (2x + 6)

12^(x² + 5x - 4) = 12^(2x + 6)

12^((x² + 5x - 4) /(2x + 6)) = 1

12^((x² + 5x - 4) -(2x + 6)) = 1

12^(x² + 5x - 4 - 2x - 6) = 1

12^(x² + 5x - 2x - 4 - 6) = 1

12^(x² + 3x - 10) = 1

ln (12^(x² + 3x - 10)) = ln(1)

(x² + 3x - 10)ln(12) = 0

ln(12) = 0 rejected

x² + 3x - 10 = 0

Now solve the quadratic equations by factorisation.

(x-2)(x+5) = 0

x = 2 , x = -5