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anonymous
 one year ago
Please help!!!!
3log(x^2) + 4log(2x)=2
anonymous
 one year ago
Please help!!!! 3log(x^2) + 4log(2x)=2

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2CAn you use the rules of logs to come up with a single log expression on the left side?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know the first couple of steps...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not sure what you're asking? Sorry.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Can you show the steps you already did?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03log(x^2) + 4log(2x)=2 log(x^2)^3 + log(2x)^4=2 log (x^6) + log (16x^4)=2

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2The last step is not correct, but until the previous step you are correct.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(3 \log x^2 + 4 \log 2x = 2\) \(\log (x^2)^3 + \log(2x)^4 = 2\) \(\log x^6 + \log (2^4 x^4) = 2\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now we use the rule of logs: \(\log a + \log b = \log (ab) \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So, log (16x^24) = 2?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(\log (x^6 \cdot 2^4x^4) = 2\) \(\log (2^4 x^{10}) = 2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh you add 6 and 4..

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Remember, when you multiply powers with the same base, you ADD the exponents.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2The rule is: \(a^m \cdot a^n = a^{m + n} \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So for the next step... log(2)= 16x^10?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Ok. Now we use the definition of log. Is this log base 10 or natural log?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Definition of log: \(\large \log_b x = y \iff b^y = x\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now let's use the last equation we have as the left side of the definition of log, and change it into the exponential version on the right side.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(\log (2^4 x^{10}) = 2~~~\iff~~~10^2 = 2^4x^{10}\) Do you understand this step?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Great. Now let's continue solving for x.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0100=16x^10 Divide 16 6.25=x^10 6.25^(1/10) x=1.2011

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(2^4x^{10} = 10^2\) \(x^{10} = \dfrac{10^2}{2^4} \) \(x^{10} = \left( \dfrac{10}{2^2} \right)^2\) \(x^{10} = \left( \dfrac{5}{2} \right)^2\) \(\left (x^{10} \right)^{\frac{1}{10}} = \left( \left( \dfrac{5}{ 2} \right)^2\ \right)^{\frac{1}{10}} \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I understand now, thanks so much!

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(x = \left( \dfrac{5}{2} \right) ^ {\frac{1}{5}} \) \(x = \sqrt[5] {\dfrac{5}{2} } \)
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