More help with Logs/Exponential functions...?

Question

I've been trying to do two problems this morning, and I can't seem to get them right. Here is one of them.

http://img338.imageshack.us/img338/7339/667vx9.png

Since it is subtraction, you have to divide (as well as combine the logs) so I get:

Log4(x^2)/(x+1) = 8

Now, to change to exponential function

4^8 = (x^2)/(x+1)

And that's when the confusion sinks in. What do I do next? Do I cross multiply? (65536)/(1) = (x^2)/(x+1)

Answer 1

ok
x^2=4^8x+4^8
x^2 -4^8x -4^8 =0

x= [4^8 +/-√(4^16+4^8 * 4 ]/2
=[4^8 +/- √(4^16+4^9)]/2
=[65536+/- 65537.999]/2
x= 65536.9999 ( ≈65537)
or x= -0.9999 (≈ -1)

Answer 2

Let log be log to base 4:-
log [ x² / (x + 1) ] = 8
x² / (x + 1) = 4^8
x² = 4^8 x + 4^8
x² - 4^8 x - 4^8 = 0
x = [ 4^8 ± √(4^16 + 4^9) ] / 2
Take + value of √(4^16 + 4^9) to obtain maximum value of x.

(nasty numbers in this question!)

Answer 3

Log4(x^2)/(x+1) = 8

log(x^2/(x+1)) = 8 ln(4) = ln(4^8)

x^2 /(x+1) = 4^8
x^2 - 4^8(x+1) =0
x^2 -4^8x -4^8 =0
D = (4)^16 +4(4)^8 = 4^8(4^8+4)
x1 = {4^8 +sqrt(4^8(4^8+4)) }/2
x2 = {4^8 -sqrt(4^8(4^8+4) ) }/2

x1 = {4^8 +4^4sqrt(4^8+4) }/2 = 65537
x2 = {4^8 -4^4sqrt(4^8+4) }/2 = -1