Is the following equation true?
lo g 2 0 1 4 ln 2 0 1 4 + ln 2 0 1 5 lo g 2 0 1 5 = ln 2 0 1 6 lo g 2 0 1 6 + lo g 2 0 1 7 ln 2 0 1 7
Here, lo g x denotes lo g 1 0 x .
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actually since log(x) means ln(x), both sides are 2.
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I think you're probably right. I assumed log(x) was equal to log base 10 of x, because that's what it means in the US. It's cool that it works either way, though.
I think most people use base-10 when they write log(x). ln(x) is base-e.
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well. base-e in calculus we dont even use base-10. see the wikipedia page on taylor series. you will find queries about natural log as log(n). also in wolfram alpha log is used as base e.
ln x is not equal to log x/log e because the base in log x is e so it is ln x only and log e is 1. ln x is equal to 2.303 times log to base 10 of x.
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Let,
n = lo g 2 0 1 4 ln 2 0 1 4 + ln 2 0 1 5 lo g 2 0 1 5 = lo g 2 0 1 4 lo g e lo g 2 0 1 4 + lo g e lo g 2 0 1 5 lo g 2 0 1 5 = lo g e 1 + lo g e
And,
m = lo g 2 0 1 7 ln 2 0 1 7 + ln 2 0 1 6 lo g 2 0 1 6 = lo g 2 0 1 7 lo g e lo g 2 0 1 7 + lo g e lo g 2 0 1 6 lo g 2 0 1 6 = lo g e 1 + lo g e
Now, we can see that n = m .