A question for all you Calculus people.?

Question

1)Solve the equation.

(1/9)^x-3 = 27^2x-1

Answer 1

(1/9)^x-3=BLAH, BLAH & ALSO
27^2X-1=BLAH, BLAH HENCE
(1/9)^x-3=27^2X-1

Answer 2

Original Problem:

(1/9)^x-3 = 27^2x-1

Convert to logs:

log(1/9)^x-3= log27^2x-1

Then use what my teacher calls the swoop rule:

x-3log(1/9)=2x-1log27

Next make the logs common logs of 3:

x-3log3^-2=2x-1log3^3

Swoop again:

-2(x-3)log3=3(2x-1)log3

Now do the Math:

-2(x-3)=3(2x-1)

Think you got it from here:

-2x+6=6x-3 --- 8x=9 --- x=(9/8)

Answer 3

Here's a clue. Think in terms of powers of 3.

Answer 4

x=9/8....it was damn simple..