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anonymous
 one year ago
Given the exponential equation 2^x = 8, what is the logarithmic form of the equation in base 10?
anonymous
 one year ago
Given the exponential equation 2^x = 8, what is the logarithmic form of the equation in base 10?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know how to write 2^x = 8 as a logarithmic equation of base 2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Exponential 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
 one year ago
Best ResponseYou've already chosen the best response.0See if you can fill in the numbers from your equation dw:1439501859795:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh so it would be log_2=8 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not quite. The 8 should be on the other side of the equation and it looks like you dropped the xdw:1439501996772:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh true so that would equal 3?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0It's like a multiple choice question so I have answer choices I can show you if you want to see them

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0What's the formula you have so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't have any right now like I don't know how to do this at all tbh

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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 itdw:1439502539460:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so log_2 8= x and then do we have to solve it or something?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no. you don't have to solve it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh nevermind we dont solve it but what do we do w it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we're going to use the change of base formula to convert it to base 10.dw:1439502646197:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So you should have \[x=\frac{ \log 8 }{ \log 2 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right so do i solve that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i have an answer choice that looks like x=log_10 2 divided by log_10 8

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would that be correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no the 8 has to be on top. Is there one that has \[x=\frac{ \log_{10} 8 }{ \log_{10}2 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes! would that be correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes That's the same thing as above, except the 10 isn't usually written because it's understood.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay thank you so much!
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