Finding x with ln(a)/ln(b) as the answer. Help needed

[hostergaard]

Homework Statement

http://img213.imageshack.us/img213/2327/nummer1.jpg

Homework Equations

The Attempt at a Solution

I find that that 3^x*4^2x+1=4*48^x
and 6^x+2=36^x

then i but ln(4*48^x)=ln(48)*x+2*ln(2)
and ln(36^x)=2*ln(6)*x
we get: ln(48)*x+2*ln(2)=2*ln(6)*x

Now my proplem is; Is this all correct and what how do i move them around so i get x? I I am really bad at moving those number around but x seems to disappear for me!

 

[slider142]

If you have trouble with this, simplify the equation in your head so that you have only x and constants which don't depend on x. In your case, ln(48)*x+2*ln(2)=2*ln(6)*x should look like Ax + B = Cx.
From algebra, you can add the same number or variable to both sides and preserve the equality:
Ax + B - Ax = Cx - Ax
B = Cx - Ax
When you are done, you can replace the dummies A, B and C with the real constants.

 

[hostergaard]

then i get 2*ln(2)=2*ln(6)*x-ln(4)4*x
2*ln(2)=2*ln(3)*x


and then i move them again:
(2*ln(2))/(2*ln(3))=(ln(2))/(ln(3))=x And that should be the answer!
Thanks!
My teacher is utterly baflet over my lack of abillity to grasp some of the simpler aspect while having no trubles with some of the more advancet aspects... But that dummy tecnique i am sure will help me out with these things in the future. Thanks a lot! :-)

 

[Gregg]

Homework Statement

http://img213.imageshack.us/img213/2327/nummer1.jpg

Homework Equations

The Attempt at a Solution

I find that that 3^x*4^2x+1=4*48^x
and 6^x+2=36^x

then i but ln(4*48^x)=ln(48)*x+2*ln(2)
and ln(36^x)=2*ln(6)*x
we get: ln(48)*x+2*ln(2)=2*ln(6)*x

Now my proplem is; Is this all correct and what how do i move them around so i get x? I I am really bad at moving those number around but x seems to disappear for me!

$6^{x+2} = 36^x$
Let x = 3
$6^5 = 7776$
$36^3 = 46,656$

$6^{x+2} = 36.6^x$

 

[kazak88]

.................
. 6^(x+2)=36^x - false - {a^(x+y)=(a^y)^x} .
. a^(x+y)=(a^x)*(a^y) - true
. only a^(x*y)=(a^y)*x...then 6^(x+2)=(6^x)*(6^2)=36*(6^x)
.................
.b
..y
...
...K
...a
...z
...a
...K
...
...R
...O

 

[Gregg]

.................
. 6^(x+2)=36^x - false - {a^(x+y)=(a^y)^x} .
. a^(x+y)=(a^x)*(a^y) - true
. only a^(x*y)=(a^y)*x...then 6^(x+2)=(6^x)*(6^2)=36*(6^x)
.................
.b
..y
...
...K
...a
...z
...a
...K
...
...R
...O

Yeah what I wrote is wrong but it was a long time ago.