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# Logarithm

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If $$\frac{^5log2}{^5log3}=m$$ , then $$2^{2m}+2^{m+2}=?$$

Thank you very much for helping me.

Apr 20, 2018

#1
+101768
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What is the little 5 for?

Apr 21, 2018
#2
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The little 5 is derived from the question itself. I don't know if the question is wrong from the beginning or not. But that what the question is. I can post a picture of it if you want.

Note : i am not a native english speaker, i am very sorry for any mispell or miscommunication. I just need help :(

Guest Apr 21, 2018
#3
+101768
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Well the 5 does not make sense but lets look at a possible meaning.

Note that  when an English speaking person sees    $$log_25$$

They would SAY it as                                        log of 5 base 2     or   log 5 base 2

$$m=\frac{log_25}{log_35}\\ m=\frac{log5}{log2}\div \frac{log5}{log3}\\ m=\frac{log5}{log2}\times \frac{log3}{log5}\\ m=\frac{log3}{log2}\\ mlog2=log3\\ log2^m=log3\\ 2^m=3\\~\\$$

$$2^{2m}+2^{m+2}\\ =(2^m)^2+2^m*2^2\\ =3^2+3*4\\ =9+12\\ =21$$

If the pic looks a little different perhaps you should post that

Apr 23, 2018
#4
+1

Thank you very much for solving it! And yes, after i did some googling, turns out there is a difference between how the english use of notation and our county use of log notation.

Guest Apr 23, 2018