Question

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

Answer 1

Answer:

x = -8

Step-by-step 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

Answer 2

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:

$x = -8$