TheEdwardsFamily
  • TheEdwardsFamily
PLEASE HELP ME!!!!!!!! I'LL MEDAL! What is the missing exponent? (10^6) ____ = 10 ^-18
Mathematics
schrodinger
  • schrodinger
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TheEdwardsFamily
  • TheEdwardsFamily
anonymous
  • anonymous
Are you familiar with logs?
TheEdwardsFamily
  • TheEdwardsFamily
no...

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anonymous
  • anonymous
I'm having trouble with the question. Is it\[(10^6)^x = 10^{-18}\]
TheEdwardsFamily
  • TheEdwardsFamily
yes
anonymous
  • anonymous
10 to the power 6 = 1,000,000 start there
TheEdwardsFamily
  • TheEdwardsFamily
im trying to find the missing exponent
anonymous
  • anonymous
OK. Then no logs required. This question involves using the laws of exponents. The law you need to understand to answer this question is the "power to a power" law. It say that when you have a power raised to another power, you multiply the exponents together. IN other words\[\left( b^n \right)^m = b^{nm}\] So, what is\[\left( 10^6 \right)^x\]
TheEdwardsFamily
  • TheEdwardsFamily
10^6 is 60
anonymous
  • anonymous
No. Leave the base (10) alone and just multiply the two exponents. What is \(6 \times x\) ?
anonymous
  • anonymous
\[\left( 10^6 \right)^x = 10^{6 \times x} = ?\]
TheEdwardsFamily
  • TheEdwardsFamily
so i am multiplying 6 * 6? im confused. (math is not my favorite subject.)
anonymous
  • anonymous
No. Multiply 6 times x. What do you get?
TheEdwardsFamily
  • TheEdwardsFamily
6?
anonymous
  • anonymous
May I ask what course this is for? What grade level?
TheEdwardsFamily
  • TheEdwardsFamily
8th grade
anonymous
  • anonymous
Have you done algebra?
TheEdwardsFamily
  • TheEdwardsFamily
yes
anonymous
  • anonymous
So have you solved problems like\[3x=18\]/etc.
TheEdwardsFamily
  • TheEdwardsFamily
yes. i have.
anonymous
  • anonymous
OK. Good. So when you see \(3x\) as above, what mathematical operation is going on between the 3 and the x? (Addition, subtraction, multiplication, division)
TheEdwardsFamily
  • TheEdwardsFamily
multiplication
anonymous
  • anonymous
Excellent. So\[3 \times x = 3x\]right?
TheEdwardsFamily
  • TheEdwardsFamily
yes
anonymous
  • anonymous
OK. Back to your question. What is \(6 \times x\) ?
TheEdwardsFamily
  • TheEdwardsFamily
mmm....im thinking 3
anonymous
  • anonymous
I'm sorry, I'm trying to determine where you're confused. You were just able to determine that\[3 \times x = 3x\] but you're having difficulty with\[6 \times x = ?\]Can you tell me what's confusing you?
TheEdwardsFamily
  • TheEdwardsFamily
ok, i think i understand now 6 * x =6x
TheEdwardsFamily
  • TheEdwardsFamily
I was just confused at the beginning
anonymous
  • anonymous
Yes! So, we've got your problem down to this:\[\left( 10^6 \right)^x = 10^{-18}\]\[10^{6 \times x} = 10^{-18}\]\[10^{6x} = 10^{-18}\]
anonymous
  • anonymous
Now at this point, we have a single power on each side of the equation and these powers have the same base, i.e. 10. So now you can forget the bases and equate just the exponents, i.e.\[6x = -18\]Can you solve this for x?
anonymous
  • anonymous
Sorry. Gotta run. Good luck finishing it off.
TheEdwardsFamily
  • TheEdwardsFamily
ok thanks for your help!

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