To solve this equation, we need to combine like terms and simplify the expression.
First, let's simplify the left side of the equation 6^(x^2 - 4x) + 6^(x^2 - 4x - 1) = 4 Let a = x^2 - 4x, then the equation becomes 6^a + 6^(a-1) = 42
Now, we can rewrite the equation as 6^a + 6^(a-1) = 6^1 * 7
Next, we can rewrite 6 as 6^1 and simplify 6^a + 6^a 6^-1 = 6^1 6^a + 6^a (1/6) = 6 6^a + 6^(a-1) = 42
Now we have simplified the equation and can see that the simplified equation matches the original equation. Therefore, the solution to the equation 6^(x^2 - 4x) + 6^(x^2 - 4x - 1) = 42 is x^2 - 4x = 1.
To solve this equation, we need to combine like terms and simplify the expression.
First, let's simplify the left side of the equation
6^(x^2 - 4x) + 6^(x^2 - 4x - 1) = 4
Let a = x^2 - 4x, then the equation becomes
6^a + 6^(a-1) = 42
Now, we can rewrite the equation as
6^a + 6^(a-1) = 6^1 * 7
Next, we can rewrite 6 as 6^1 and simplify
6^a + 6^a 6^-1 = 6^1
6^a + 6^a (1/6) = 6
6^a + 6^(a-1) = 42
Now we have simplified the equation and can see that the simplified equation matches the original equation. Therefore, the solution to the equation 6^(x^2 - 4x) + 6^(x^2 - 4x - 1) = 42 is x^2 - 4x = 1.