256^(x+2)=16^(3x-1) How do I solve this equation for x? Help is appreciated. Thank You

Guest Feb 10, 2015

#1**+10 **

256^(x+2)=16^(3x-1)

Notice that 256 = 2^8 and 16 = 2^4

So we have

2^8^(x + 2) = 2^4^(3x -1) and dropping the equal bases and solving for the exponents, we have

8(x + 2) = 4(3x - 1)

8x + 16 = 12x - 4 add 4 to both sides and subtract 8x from both sides

20 = 4x divide both sides by 4

5 = x

CPhill
Feb 10, 2015

#1**+10 **

Best Answer

256^(x+2)=16^(3x-1)

Notice that 256 = 2^8 and 16 = 2^4

So we have

2^8^(x + 2) = 2^4^(3x -1) and dropping the equal bases and solving for the exponents, we have

8(x + 2) = 4(3x - 1)

8x + 16 = 12x - 4 add 4 to both sides and subtract 8x from both sides

20 = 4x divide both sides by 4

5 = x

CPhill
Feb 10, 2015