Question

Solve the following equation algebraically. 9^(x-2)=(1/27)^(x+4)

Answer 1

Create equivalent expressions in the equation that all have equal bases.32(x+2)=3−3(x+12)32⁢x+2=3-3⁢x+12Since the bases are the same, then two expressions are only equal if the exponents are also equal.2(x+2)=−3(x+12Simplify the left side.2x+4=−3(x+12)2⁢x+4=-3⁢x+12
Simplify the right side.2x+4=−3x−362⁢x+4=-3⁢x-36



x=−8

Answer 2

Answer:

-1.6=x

Step-by-step explanation:

First, find a common base.

A common base of 9 and 27 is 3.

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

Simplify

3^(2x-4) = 3^(-3x-12)

Take away the common bases

2x-4 = -3x-12

Add 12 to both sides

2x+8 = -3x

Subtract 2x from both sides

8 = -5x

Divide both sides by -5

-1.6 = x

Answer: -1.6 = x