anonymous
  • anonymous
Given the exponential equation 2^x = 8, what is the logarithmic form of the equation in base 10?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
help will medal you
anonymous
  • anonymous
Do you know how to write 2^x = 8 as a logarithmic equation of base 2?
anonymous
  • anonymous
i do not

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anonymous
  • anonymous
Exponential and logarithmic forms are just two different ways to write the same equation. For example, we know that \(3^2=9\). That is the exponential form of the equation. The log from is \(\log_{3} 9=2\). They mean exactly the same thing. This is how you go from one form to the other |dw:1439501752391:dw|
anonymous
  • anonymous
See if you can fill in the numbers from your equation |dw:1439501859795:dw|
anonymous
  • anonymous
oh so it would be log_2=8 ?
anonymous
  • anonymous
not quite. The 8 should be on the other side of the equation and it looks like you dropped the x|dw:1439501996772:dw|
anonymous
  • anonymous
oh true so that would equal 3?
anonymous
  • anonymous
Yes, x does equal 3, but it doesn't look like they want you to solve for it. They want you to rewrite the equation, but keep the x
anonymous
  • anonymous
It's like a multiple choice question so I have answer choices I can show you if you want to see them
anonymous
  • anonymous
I don't really need them. Once you have the log equation with base 2 all we have to do is use the change of base formula to convert it to base 10.
anonymous
  • anonymous
What's the formula you have so far?
anonymous
  • anonymous
I don't have any right now like I don't know how to do this at all tbh
anonymous
  • anonymous
I put a graphic up. Follow the arrows to put the numbers/variables in the right place to convert the equation from exponential to logarithmic. Here it is in case you missed it|dw:1439502539460:dw|
anonymous
  • anonymous
so log_2 8= x and then do we have to solve it or something?
anonymous
  • anonymous
no. you don't have to solve it
anonymous
  • anonymous
oh nevermind we dont solve it but what do we do w it?
anonymous
  • anonymous
we're going to use the change of base formula to convert it to base 10.|dw:1439502646197:dw|
anonymous
  • anonymous
So you should have \[x=\frac{ \log 8 }{ \log 2 }\]
anonymous
  • anonymous
right so do i solve that?
anonymous
  • anonymous
that's the answer
anonymous
  • anonymous
oh i have an answer choice that looks like x=log_10 2 divided by log_10 8
anonymous
  • anonymous
would that be correct?
anonymous
  • anonymous
no the 8 has to be on top. Is there one that has \[x=\frac{ \log_{10} 8 }{ \log_{10}2 }\]
anonymous
  • anonymous
yes! would that be correct?
anonymous
  • anonymous
Yes That's the same thing as above, except the 10 isn't usually written because it's understood.
anonymous
  • anonymous
oh okay thank you so much!
anonymous
  • anonymous
you're welcome

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