Question

Решите уравнение. 3^2x-6=1

Answer 1

$3 {}^{2x- 6} = 1 \\ 3 {}^{2x - 6} = 3 {}^{0 } \\ 2x - 6 = 0 \\ 2x = 6 \\ x = 3$

Answer 2

По моим расчетам все правильно

Answer 3

To solve the equation 3^(2x) - 6 = 1, follow these steps:

Step 1: Move the constant term to the other side of the equation:

3^(2x) = 1 + 6 3^(2x) = 7

Step 2: Take the logarithm of both sides to get rid of the exponent:

log(3^(2x)) = log(7)

Step 3: Apply the logarithm property log(a^b) = b * log(a):

2x * log(3) = log(7)

Step 4: Divide both sides by log(3) to isolate 2x:

2x = log(7) / log(3)

Step 5: Finally, divide by 2 to solve for x:

x = (log(7) / log(3)) / 2

Using a calculator to compute the values, we get:

x ≈ 0.7732