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Number Theory Level 2

find x value for which x. logx=log256


The answer is 4.

Madhav Srirangan by madhav srirangan , 20, India

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3 solutions

Sudoku Subbu
Mar 6, 2015

given , x l o g x = l o g 256 xlogx=log256 consider RHS l o g 256 = l o g 4 4 = 4 l o g 4 = x l o g x log256=log4^4=4log4=xlogx therefore the value of x is 4

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Vishal S
Feb 25, 2015

xlogx=log256

=>logx^x=log256

=>x^x=256

=>256=4^4

=>x=4

0 Helpful 0 Interesting 0 Brilliant 0 Confused

good solution so only i tried in another manner cheers, subbu

sudoku subbu - 6 years, 3 months ago

vishal you are an amazing guy

Math Special - 4 years, 11 months ago

The equation can be re-written as

x x = 256 = 2 8 = 4 4 x^x=256=2^8=\boxed{4^4}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

oh! you removed log and done in algebraic manner good i like this even

sudoku subbu - 6 years, 3 months ago

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