Can you proof this identity briefly enough?

without posting links please.

Question

Can you proof this identity briefly enough?

without posting links please.

solomonzelman · Answer

$$\huge\color{blue}{\huge {\bbox[5pt,lime,border:2px solid purple]{Log_27=\frac{Log_{10}7}{Log_{10}2}}}}$$

solomonzelman · Answer

I am leaving for an hour..

anonymous · Answer

change of base theorem
I suck at proofs :(

mathstudent55 · Answer

$ \log_2 7 = x \iff 2^x = 7$

$\log_{10} 7 = y \iff 10^y = 7$

$y = \log_{10} 7 $

$~~= \log_{10}{2^x} $

$~~= x\log_{10}{2}$

$ y= \log_2 7 \log_{10} 2$

$ \log_{10} 7= \log_2 7 \log_{10} 2$

$ \dfrac{\log_{10}7 }{\log_{10} 2} = \log_2 7$

solomonzelman · Answer

WOW! NICE AND CLEAR!

mathstudent55 · Answer

wlcm

solomonzelman · Answer

@jim_thompson5910 @phi @myininaya

can you give math student a medal for appreciation?

solomonzelman · Answer

Really awesome, and brief I like that, and without unnecessary words...

anonymous · Answer

how do you give medals?

mathstudent55 · Answer

It's just the definition of logs, a property of logs, and substitution. Then a little algebra to finish it off.

myininaya · Answer

Yes. You can give medals to students. I do sometimes when they put forth a good effort.