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

Question

asked Nov 18, 2020 34.2k views

2 Answers

Thiago Jackiw · Answer 1 · 2020-11-19T23:41:33+0000

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:

Rob Farr · Answer 2 · 2020-11-23T19:49:24+0000

Answer:

x = -8

Explanation:

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

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

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