anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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hartnn
  • hartnn
you can't cancel the 6's ....as u suspected
anonymous
  • anonymous
yes don't cancel the six
hartnn
  • hartnn
1/6 = 6^{-1} then compare the exponents

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anonymous
  • anonymous
Thankyou so much, so what happens instead of that?
anonymous
  • anonymous
a^m/ a^n =a^m-n
hartnn
  • hartnn
fitst simplify 6^(....)/6^(...) using that ^
anonymous
  • anonymous
so 6 ^4x-2-(3x-6)
hartnn
  • hartnn
\(\huge 6^{(4x+2)-(3x-6)}=...?\)
anonymous
  • anonymous
therefore 6^(4x-2-3x+6)=1/6
anonymous
  • anonymous
6^(x+4)=1/6
anonymous
  • anonymous
Thank-you so much! I get it now :)
anonymous
  • anonymous
1/6 = 6^-1
hartnn
  • hartnn
\(\huge 6^{(4x+2)-(3x-6)}=6^{-1} \\ \huge \implies (4x+2)-(3x-6)=-1 \)
anonymous
  • anonymous
x+4 =-1 therefore x =3
hartnn
  • hartnn
actually x+8 = -1
hartnn
  • hartnn
its 4x+2, not 4x-2 :)
anonymous
  • anonymous
So I got 3 for my answer, but the textbook says -9...
Yttrium
  • Yttrium
it's -9 @student.1 since you're gonna distribute the negative sign at 3x-6
hartnn
  • hartnn
how u got 3 ?
Yttrium
  • Yttrium
so what will happen is that it'll become 4x+2-3x+6 = -1 x+8 = -1 Therefore, x =-9
anonymous
  • anonymous
OH thanks

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