Question

Solve the following equation:

`4^(x^2) : 4^x = 16 : 1`

Answer 1

Given: `4^(x^2) : 4^x = 16 : 1`

Step-wise calculation:

Step 1: Use the property of exponents `a^m/a^n = a^(m - n)` to simplify the left-hand side: 

`4^(x^2 - x) = 16`

Step 2: Express 16 as a power of 4:

16 = 4²

Step 3: Equate the exponents since the bases are the same and both sides are positive:

x² – x = 2

Step 4: Rearrange the equation:

x² – x – 2 = 0

Step 5: Factorize the quadratic equation:

(x – 2)(x + 1) = 0

Step 6: Solve for (x):

x = 2 or x = –1

The solutions to the equation are x = 2 or x = –1.