anonymous
  • anonymous
log{b} 1000=3 I know b=10 but I don't understand how they got there.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\log_{b} 1000=3\]
anonymous
  • anonymous
\[b^3=1000\] \[3\sqrt{b^3}= 3\sqrt{1000}\] b=10
Nnesha
  • Nnesha
well did you take 3rd root right ? you can write 1000 in terms of 3 exponents

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Nnesha
  • Nnesha
x^3 =1000 ? what is x
anonymous
  • anonymous
10
anonymous
  • anonymous
What is the point of the 3's in front of the square root signs?
Nnesha
  • Nnesha
that's not 3 it's a 3rd rooot i guess like this \[\huge\rm \sqrt[3]{b^3}\]
anonymous
  • anonymous
Right, I didn't know how to do that
Nnesha
  • Nnesha
you can convert 3rd to 1/3 exponent \[\huge\rm \sqrt[3]{b^3} = b^{3 \times \frac{ 1 }{ 3 }}\] so cancel out 3 exponent u have to take 3rd root :=)
Nnesha
  • Nnesha
\[\huge\rm \sqrt[3]{b^3} = b^{\cancel3 \times \frac{ 1 }{\cancel 3 }}=b\]
anonymous
  • anonymous
Wouldn't that also mean that 1000 would be multiplied by 1/3?
Nnesha
  • Nnesha
yes so 1000 can be written as 10 to the 3rd power \[\huge\rm \sqrt[3]{10^3}\]
anonymous
  • anonymous
See that's where I get confused, so the 1000 get simplified down to 10 because?
Nnesha
  • Nnesha
because it's easy to solve without calculator and it's legal :3
anonymous
  • anonymous
-_- so because 10^3=1000 it gets simplified to 10^3 and since it's the 3rd root the exponent cancels out leaving b=10 ?
Nnesha
  • Nnesha
b to the 3rd power so you can either write 10 to the 3rd power or put 3rd root of 1000 into the calculator :=)
Nnesha
  • Nnesha
yep
anonymous
  • anonymous
See when I enter that into my calc I get 94.86....
Nnesha
  • Nnesha
and it's helpful when you have to find an exponent given base for example 10^x = 1000
Nnesha
  • Nnesha
what did you enter ?
freckles
  • freckles
\[3 \sqrt{1000} \neq \sqrt[3]{1000}\]
anonymous
  • anonymous
\[3\sqrt{1000}\]
anonymous
  • anonymous
Yea see I don't know how to enter the latter
Nnesha
  • Nnesha
it's not 3 times square root of {1000} 3rd root like \[\sqrt[3]{1000}\]
Nnesha
  • Nnesha
ohh then convert 3rd root to 1/3 exponent \[\huge\rm \sqrt[3]{1000} = (1000)^\frac{ 1 }{ 3 }\]
anonymous
  • anonymous
That works. =] Could you possibly help me with another problem?
Nnesha
  • Nnesha
gtg :3 sorry
anonymous
  • anonymous
All's well Thank you for your help :)
Nnesha
  • Nnesha
my pleasure

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