anonymous
  • anonymous
If (9^2)p = 9^8, what is the value of p? 2 3 4 6
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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DanJS
  • DanJS
is p also a power of that 9^2 term?
anonymous
  • anonymous
Yes @DanJS
DanJS
  • DanJS
\[[9^2]^p = 9^8\]

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DanJS
  • DanJS
recall, a power raised to a power is simplified by multiplying the powers [9^2]^p = 9^(2*p)
DanJS
  • DanJS
Since you have the same bases raised to different powers, you can equate the powers from both sides 2p = 8
DanJS
  • DanJS
Or if you need work, take the log base 9 of both sides, move the powers down in front...
anonymous
  • anonymous
So its D? Or did I do my math wrong?
DanJS
  • DanJS
2p = 8
DanJS
  • DanJS
\[9^{2p}=9^8\] \[\log_{9}9^{2p} = \log_{9}9^8 \] \[(2p)*\log_{9}9 = 8 * \log_{9}9\] \[2p * 1 = 8*1~~~~~~~~~~~;p=4\]

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