Question

9^x = 3^(1-2x)
What is x?
Explain to me how to do these ridiculous problems with the exponents being all subtracted.

Answer 1

trick is to write with the same base, then compare exponents

Answer 2

you have
\[9^x\] and
\[9=3^2\] so this is
\[(3^2)^x=3^{2x}\]

Answer 3

so the left hand side is
\[3^{2x}\] right hand is
\[3^{1-2x}\] so
\[3^{2x}=3^{1-2x}\] ,making
\[2x=1-2x\] solve for x

Answer 4

point is not the exponents being subtracted, point is making them equal to see what you get for x. you get
\[4x=1\]
\[x=\frac{1}{4}\]

Answer 5

You're the best, thank you! Makes much more sense now!

Answer 6

thx
and yw