Question

which equation has x = –6 as the solution?log subscript x baseline 36 = 2log subscript 3 baseline (2 x minus 9) = 3log subscript 3 baseline 216 = xlog subscript 3 baseline (negative 2 x minus 3) = 2

Answer 1

The correct answer is log3(-2x-3)=2

Answer 2

log₃(-2x - 3) = 2

Explanation:

logₓ(36) = 2:

To solve this equation, we need to find the value of x for which logₓ(36) equals 2. Rewriting this equation in exponential form, we have x² = 36. Taking the square root of both sides gives us x = 6.

log₃(2x - 9) = 3:

3^(log₃(2x - 9)) = 3³

By applying the property of logarithms that states logₓ(x^a) = a, we can simplify the equation further:

2x - 9 = 27

Now, let's solve for x:

2x = 27 + 9

2x = 36

x = 36/2

x = 18

log₃(216) = x:

log₃(6³) = x

3log₃(6) = x

3 + 3log₃(2) = x

log₃(-2x - 3) = 2:

- 2x - 3 = 3²

- 2x - 3 = 9

- 2x + 3 = 9 + 3

- 2x = 9 + 3

- 2x = 12

- 2x / -2 = 12/-2

x = -6

In summary, the equation that has x = -6 as the solution is the last equation: log₃(-2x - 3) = 2