Question

What is the answer for 27^x=9^x-4

Answer 1

For this case we must solve the following equation:

`27 ^ x = 9 ^ {x-4}`

We rewrite:

`27 = 3 * 3 * 3 = 3 ^ 3\\9 = 3 * 3 = 3 ^ 2`

So:

`3^(3(x))=3^(2(x-4))`

Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:

`3 (x) = 2 (x-4)\\3x = 2x-8`

Subtracting 2x on both sides:

`3x-2x = -8\\x = -8`

Answer:

`x = -8`

Answer 2

x = -8

Explanation:

We are given the following expression which we are to solve for
`x`:

`2 7 ^ x = 9 ^ { x - 4 }`

For this expression, we will make the bases same on both sides of the equation and then equate the exponents equal to each other.

`(3^3)^x = (3^2)^(x-4)`

Multiplying the exponents and equating them to get:

`3 x = 2 ( x - 4 )`

`3 x = 2 x - 8`

`3 x - 2 x = - 8`

x = -8