Solving Math Problems?

Question

I am having some real hard troubles with rational expressions and things like that. How would I solve this equation to find x. Please give all the steps and explain if possible.

http://img216.imageshack.us/img216/312/problemza1.jpg

Answer 1

8^x+3=16^2x+3 factor 2 raised to x power
(2^3)^x+3=(2^4)^2x+3{cancel 2 and leavepower}
3x+9=8x+12 factor out powers

x=(3/-5)

Answer 2

Equations with exponents are solved by using logarithms. In your problem, take the logarithm of both sides to get

(x+3)*log(8) = (2x+3)*log(16)

log(8) and log(16) are just numbers. You should be able to sove for x.

In this case there is an even easer way: recognize that 8 = 2^3 and 16=2^4. You get 2^(3x+9) = 2^(8x+12); the powers are then equal: 9+3x = 8x+12

Either method works

Answer 3

first you want to make the bases the same.
(2^3)^(x+3)=(2^4)^(2x+3)
Then you multiply the exponents together.
2^(3x+9)=2^(8x+12)
You can then remove the bases and solve for x.
3x+9=8x+12
Subtract 3x from both sides
9=5x+12
Subtract 12 from both sides
-3=5x
divide by 5 and therefore:
(-3/5)=x

Answer 4

8^(x+3) = 16^(2x+3) is the same as

(2^3)^(x+3) = (2^4)^(2x+3) so, by the laws of exponents
2^(3x+9) = 2^(8x+12) and so
3x+9 = 8x+12 and
x = -3/5


Doug

Answer 5

8^(x+3)=16^(2x+3)
because of 8=2^3 and 16=2^4, so
2^3(x+3)=2^4(2x+3)
from this equation, we can create another equation,
>>> 3(x+3)=4(2X+3)
3x+9=8x+12
-3=5x
so x=-3/5

have fun, good luck.

Answer 6

8^(n + 3) = 16^(2n + 3)
(2^3)^(n + 3) = (2^4)^(2n + 3)
2^(3(n + 3)) = 2^(4(2n + 3))
2^(3n + 9) = 2^(8n + 12)

therefore

3n + 9 = 8n + 12
-5n = 3
n = (-3/5)