An algebra problem by Hobart Pao

Algebra Level 3

[ log ⁡ 37 − 6 ( 37 + 6 ) ] 9999 P 9997 \left[ \log_{ \sqrt{ 37} - 6 } ( \sqrt{ 37 } + 6 ) \right] ^ { _{9999} P _{9997} }

Evaluate the expression (P for permutations as in nPr):


The answer is 1.

Hobart Pao by Hobart Pao , 23, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

U Z
Sep 26, 2014

37 + 6 = 1 37 − 6 \sqrt{37} +6 = \frac{1}{ \sqrt{37} - 6}

thus we have to find (-1) raise to the power which is an even number thus answer = 1

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice problem!

milind prabhu - 6 years, 7 months ago

Nicotinamide, there is slight ambiguity in the expression, which could have been interpreted as ( log ⁡ 37 ) + 6 (\log \sqrt{ 37} ) + 6 or log ⁡ ( 37 + 6 ) \log ( \sqrt{ 37} + 6 ) . I've updated the question so that this is made clear.

Calvin Lin Staff - 6 years, 6 months ago

Log in to reply

OK thanks!

Hobart Pao - 6 years, 6 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...