ay i have looked at this problem for days and i can't figure it out?

Question

3 to the power of x+2 equals 7 to the power of 2x plus 5

Answer 1

3^(x+2)=7^(2x+5)
(x+2)log 3 = (2x+5)log 7
xlog3 +2log 3= 2xlog 7 + 5log 7
x(log3-2log 7)=5log 7 - 2 log 3
x= (5 log 7 - 2 log 3)/(log 3 - 2 log 7)
x= (4.225-.954)/(.477- 1.69)
x= -2.6966

Answer 2

Alright, so it sounds like you want to solve for x in the equation:
3^(x+2) = 7^(2x+5)
I would first take the natural log of both sides (or any log really).
So:
ln3^(x+2) = ln7^(2x+5)

Now you can take the powers and bring them in front of the logs because of log properties. So:

(x+2)ln3 = (2x+5)ln7, distribute.
xln3 + 2ln3 = 2xln7 + 5ln7, isolate x on both sides.
xln3 - 2xln7 = 5ln7 - 2ln3, factor out an x
x(ln3-2ln7) = 5ln7 - 2ln3
x = (5ln7 - 2ln3)/(ln3-2ln7)

Check this, but I think that comes out to about -2.6967. Hope that's helpful.

Answer 3

Offhand, it looks like x will negative for this to work.
A quicky way to do this is to find 7 to the base 3. You can use base 10 logs for this = log 7/log 3. Call result "A" (about 1.7). Then you can set
A * (2x+5) = x+2 and solve for x in terms of A and numbers. (2-5A )/ (2A-1) ???

Answer 4

3^(x + 2) = 7^(2x + 5)
Take the ln of both sides

ln 3^(x + 2) = ln 7^(2x + 5)

use the power rule of logs
(x + 2) ln3 = (2x + 5) ln 7

distribute
x ln3 + 2 ln3 = 2x ln7 + 5 ln7

get your x terms on same side, non-x terms on opposite side
x ln3 - 2x ln 7 = 5 ln7 - 2 ln3

factor out x on the left
x(ln3 - 2ln7) = 5ln7 - 2 ln3

divide the ( ) to other side

x = (5ln7 - 2ln3)/(ln3 - 2ln7)

Answer 5

okay...?
what's the problem? do you need to simplify it?