Oh my log!

Algebra Level 4

Given that ${ a }^{ 2 }={ b }^{ 3 }={ c }^{ 5 }={ d }^{ 6 }$ ,

let $\log _{ d }{ abc } = \frac { m }{ n }$ where m and n are co-prime integers

then $\frac { { tan }^{ -1 }(m) }{ n } =\quad ?$

give your answer to 2 decimal places. Calculate in radians.

The answer is 0.31.

1 solution

Apoorv Padghan
Aug 8, 2014

Seems easy no ? I got one of the solutions from my Buddy @Dinesh Chavan ....... As we have an equal to sign .... have everything in terms of (d) as this is the base we are asked so we get a={ d }^{ 3 }\ b={ d }^{ 2 }\ c={ d }^{ rac{ 6 }{ 5 } } so now use property of log and get log_{ d }{ { d }^{ rac{ 31 }{ 5 } } } =rac{ 31 }{ 5 } now get tan inverse of 31 and divide by 5 .turns out to be 17.63 approx

The answer should be $0.31$ because the function $f(x)=\tan^{-1} x$ will give the function values in radians. If you wanted the answer to be in degrees, then you should've specified it in the question.

Prasun Biswas - 6 years, 6 months ago

Prasun, please mind your language. Treat others with respect. I have edited your comment.

I have updated the answer to 0.31, and specified that calculations are to be done in radians.

In future, if you spot any errors with a problem, you can “report” it by selecting the “dot dot dot” menu in the lower right corner.

Calvin Lin Staff - 6 years, 6 months ago

Oh, sorry for that. I was just a bit pissed off at that time. I went into rage mode then. :P Sorry again. :)

Prasun Biswas - 6 years, 5 months ago

Oh my log!

The answer is 0.31.

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