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anonymous
 one year ago
What is the value of x in the equation.... (logarithms), equation will be posted in comments
anonymous
 one year ago
What is the value of x in the equation.... (logarithms), equation will be posted in comments

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\log_{8}x + \log_{4}x = 10/3 \]

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1Firstly, the law: \[\Large\log_ab=\dfrac{\log_nb}{\log_na}\] Substitute \(\Large a=8\), \(\Large b=x\) to get: \[\Large\log_8x=\dfrac{\log_nx}{\log_n8}\]

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1Substitute \(\Large a = 4\), \(\Large b = x\) to get: \[\Large\log_4x=\dfrac{\log_nx}{\log_n4}\]

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1What would be a reasonable \(\Large n\) to fit in?

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \log_8x+\log_4x=\dfrac{10}3\] \[\Large \dfrac{\log_nx}{\log_n8}+\dfrac{\log_nx}{\log_n4}=\dfrac{10}3\] I would actually choose \(\Large n = 2\) because \(\Large 4=2^2\) and \(\Large 8=2^3\)

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1Let's use \(\Large n = 10\) anyway.

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \dfrac{\log_{10}x}{\log_{10}2^3}+\dfrac{\log_{10}x}{\log_{10}2^2}=\dfrac{10}3\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I was debating whether to use 2, but I didn't know how to use the 2 to the power of 2 and 3 in the equation.

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1okay, let's use \(\Large n = 2\) then.

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \dfrac{\log_2x}{\log_22^3}+\dfrac{\log_2x}{\log_22^2}=\dfrac{10}3\]

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \dfrac{\log_2x}3+\dfrac{\log_2x}2=\dfrac{10}3\]

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1Are you able to find \(\Large \log_2x\) now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I'm not completely sure how to finish it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would we simplify them into one fraction?

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1Let's substitute \(\Large a \) as \(\Large \log_2x\).

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1The equation then becomes: \[\Large\frac a3+\frac a2=\frac{10}3\]

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1So \(\Large \log_2x=4\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Haha, girl  Thank you so much!
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