Question

Solve: 6ˣ⁺²=7x. enter an exact answer or round your answer to the nearest tenth.

Answer 1

To solve the equation 6ˣ⁺² = 7x, we need to isolate the variable x. The solutions to the equation are x = 0 and x ≈ 1.0827 (rounded to the nearest tenth).

Step-by-step explanation:

To solve the equation 6ˣ⁺² = 7x, we need to isolate the variable x. Here are the steps:

1. Start by subtracting 7x from both sides of the equation: 6ˣ⁺² - 7x = 0
2. Next, combine like terms: 6ˣ⁺² - 7x = 0
3. Factor out x: x(6ˣ - 7) = 0
4. Now we have two cases to consider:
   • x = 0
   • 6ˣ - 7 = 0
5. Solving the first case, we find x = 0.
6. Solving the second case, we add 7 to both sides and then take the natural logarithm of both sides to isolate x: 6ˣ = 7 => x = ln(7)/ln(6)

So the solutions to the equation are x = 0 and x ≈ 1.0827 (rounded to the nearest tenth).