Solve the equation. Put only integers or decimals for your answer.

Question

Solve the equation. Put only integers or decimals for your answer. $$ 6^{-3 x}=216 $$

UpStudy AI · Accepted Answer

The given equation is:

$$
6^{-3x} = 216
$$

First, recognize that $$216$$ can be expressed as a power of 6:

$$
216 = 6^3
$$

Now, substitute this into the original equation:

$$
6^{-3x} = 6^3
$$

Since the bases are the same, we can equate the exponents:

$$
-3x = 3
$$

Solving for $$x$$:

$$
x = \frac{3}{-3} = -1
$$

**Answer:** 
$$-1$$
$$ x = -1 $$

Upstudy AI Solution