Question

Index law help please! Find x:
36^2x+1 / 216^x-2 = 1/6

In the textbook it says the answer is -9, but I got something completely different. Here is what I did, please tell me what I'm doing wrong, thankyou!

(6^2)^2x+1/(6^3)^x-2 = 1/6
6^4x+2 / 6^3x-6 = 1/6
4x+2 / 3x-6 = 1/6 (here i cancelled the 6's-not right I don't think.)
1x-4 = 1/6 (used index law of a^m/ a^n = a^m-n)
therefore, x=-10

Please & thankyou

Answer 1

you can't cancel the 6's ....as u suspected

Answer 2

yes don't cancel the six

Answer 3

1/6 = 6^{-1}
then compare the exponents

Answer 4

Thankyou so much, so what happens instead of that?

Answer 5

a^m/ a^n =a^m-n

Answer 6

fitst simplify 6^(....)/6^(...) using that ^

Answer 7

so 6 ^4x-2-(3x-6)

Answer 8

\(\huge 6^{(4x+2)-(3x-6)}=...?\)

Answer 9

therefore 6^(4x-2-3x+6)=1/6

Answer 10

6^(x+4)=1/6

Answer 11

Thank-you so much! I get it now :)

Answer 12

1/6 = 6^-1

Answer 13

\(\huge 6^{(4x+2)-(3x-6)}=6^{-1} \\ \huge \implies (4x+2)-(3x-6)=-1 \)

Answer 14

x+4 =-1 therefore x =3

Answer 15

actually x+8 = -1

Answer 16

its 4x+2, not 4x-2 :)

Answer 17

So I got 3 for my answer, but the textbook says -9...

Answer 18

it's -9 @student.1 since you're gonna distribute the negative sign at 3x-6

Answer 19

how u got 3 ?

Answer 20

so what will happen is that it'll become
4x+2-3x+6 = -1
x+8 = -1
Therefore,
x =-9

Answer 21

OH thanks