wach
  • wach
How does 3^x + 3^x + 3^x = 3^x+1 ?
Mathematics
chestercat
  • chestercat
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asnaseer
  • asnaseer
it is making use of the rule:\[a\times a^n=a^{n+1}\]
asnaseer
  • asnaseer
can you see how?
wach
  • wach
Not really. Could you put the equation into that rule? I think I'l be able to understand, then.

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asnaseer
  • asnaseer
ok, first of all how can you simplify the left hand side of your expression?
asnaseer
  • asnaseer
e.g. a + a + a = ?
wach
  • wach
3(3^x), right?
asnaseer
  • asnaseer
correct
asnaseer
  • asnaseer
now apply the rule
waleed_imtiaz
  • waleed_imtiaz
Lets see this question like this.... :) let 3^x=y..... the above equation is....... 3^x + 3^x + 3^x = 3^x *3 y+y+y=y(3) 3y=3y...... It is an identity...... :DA
wach
  • wach
a(a^n) = a^n+1 3(3^x) = 3^x+1 Aa. If I may ask, how does the rule work/make sense?
asnaseer
  • asnaseer
e.g.:\[a\times a^3=a\times(a\times a\times a)=a\times a\times a\times a=a^4\]
asnaseer
  • asnaseer
and 4 = 3 + 1
asnaseer
  • asnaseer
the general rule here is:\[a^m\times a^n=a^{m+n}\]
wach
  • wach
Ohhhh. That makes complete sense when worked out. Thank you so much for helping me with this concept, asnaseer!
asnaseer
  • asnaseer
yw :)

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