Question

`3^(x+4) = 27^x`

∴ x = ______.

Options

• 2

• 3

• 4

• 6

Answer 1

∴ x = 2.

Explanation:

We are given the equation:

`3^((x+4)) = 27^x`

Step 1: Rewrite 27 as a power of 3

We know that:

27 = 3³

Thus, we can rewrite 27^x as:

27^x = (3³)^x = 3^3x

Step 2: Substitute and simplify

Now the equation becomes:

`3^((x + 4)) = 3^(3x)`

Step 3: Since the bases are the same, equate the exponents:

x + 4 = 3x

Step 4: Solve for x

Subtract x from both sides:

4 = 2x

Divide both sides by 2:

x = 2

Thus, the value of x is 2.