Question

Can someone explain to me how this expression works? (problem posted below)

I know that it's equal, but I'm trying to figure out how exactly it is. Can someone explain that to me?

Answer 1

\[\Large \dfrac{\log_3(5)}{\log_3(11)} = \log_{11} 5\]

Answer 2

So \[\Large 11^{1.3\cdot \frac{\log_3 5}{\log_3 11}} = (11^{\log_{11}5})^{1.3} = \boxed{5^{1.3}}\]

Answer 3

Is this clear? @gaberdeen

Answer 4

I think so . . . give me a moment to look at it, and I'll let you know.

Answer 5

I'm still a bit confused . . . could you go through step by step while explaining why you did each step?

Answer 6

Sorry, my internet is horrible right now. Do you want me to show you steps again more clearly or is there certain part you need me to explain?

Answer 7

Can you show me the steps again more clearly? Then I'll see if there's a certain part . . . I think there probably is, but I can't pinpoint it right now.

Answer 8

Okay, since \(\Large \dfrac{\log_35}{\log_3 11} = \log_{11}5\), \[\Large 11^{1.3\cdot\frac{\log_35}{\log_3 11}} = 11^{1.3\cdot\log_{11}5}\]
Using Power of a Power Property \(\Large a^{bc}= (a^b)^c\)
\[\Large 11^{1.3\cdot\log_{11}5} = (11^{\log_{11}5})^{1.3}\]
\(\large 11^{\log_{11}5}\) can be simplified to just 5.
Hence \(\Large (11^{\log_{11}5})^{1.3} = \boxed{5^{1.3}}\)

Does that help?

Answer 9

Ok, so I think the only part I need clarification on now is the first part. Do the log 3's cancel out to make log11(5)?

Answer 10

well, basically, yeah. There is rule says that \(\dfrac{\log_a b}{\log_a c} = \log_c b\)

Answer 11

Oohhh, I see. That explains a lot, ehe. Thank you so much for your help, I really appreciate it.

Answer 12

You are welcome, glad I helped