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anonymous
 one year ago
Which of the following shows the extraneous solution to the logarithmic equation below?
log3(18x^3)log3(2x)=log3(144)
x=16
x=8
x=4
x=2
I know C is not the extraneous solution, because that is the valid solution
anonymous
 one year ago
Which of the following shows the extraneous solution to the logarithmic equation below? log3(18x^3)log3(2x)=log3(144) x=16 x=8 x=4 x=2 I know C is not the extraneous solution, because that is the valid solution

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0well doesn't extraneous mean that it maybe a solution but when you check it, the solution doesn't exist... so substitute you solution into the original equation.... you need to remember that you can't take the log of a negative number....

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0so substitute your choice for a valid solution into the original equation and see if it works..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you maybe work out the full problem for me? Because I'm not really sure of the other solution options other than 4 and 4.

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0ok... x = 4 as a solution \[\log_{3}[18 \times (4)^3]  \log_{3}[2 \times (4)] = \] what is the value of the numbers inside the square brackets..?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0one of the fundemental rules for working with logs is that you can't take the log of a negative number..... so think about that as you calculate the values.. of \[18 \times (4)^3 ~~and~~ 2 \times (4) \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01152 and 8. So would the answer to the problem be 8?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0no... the fact is now you are looking at \[\log_{3}(1152)  \log_{3}(8)\] and as I said previously you can't take the log of a negative number... so while x = 4 is a solution to the equation when simplified, the fact that when you substitute it into the original equation you end up with \[\log_{3}(1152)  \log_{3}(8) = \log_{3}(144)\] it doesn't work... as an example calculate ln(5) what do you get...?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0when you put the positive solution in x = 4 you get \[\log_{3}(1152)  \log_{3}(8) = \log_{3}(144)\] which is correct...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what would the answer be then, since 8 or 8 does not work?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0the extraneous solution is x = 4 since you can't take the log of a negative number..... as I've said previously. x = 4 is a valid solution....
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