Tricky X

Algebra Level 3

If x > 2 x>2 , what is the value of x x if x = 50 log ⁡ 10 x x = 50 \log_{10} x ?


The answer is 100.

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Kandarp Singh by Kandarp Singh , 22, India

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2 solutions

Majed Musleh
May 26, 2015

x = 50 l o g ( 10 ) x x=50log_(10) x

x = 50 l o g ( x ) l o g ( 10 ) x= \frac{50 log(x)}{log(10)}

= > x l o g ( x ) = 50 l o g ( 10 ) => \frac{x}{log(x)}=\frac{50}{log(10)}

= 2 ∗ 50 2 ∗ ( l o g ( 10 ) ) = 100 l o g ( 1 0 2 ) =\frac{2*50}{2*(log(10))}=\frac{100}{log(10^2)}

x l o g ( x ) = 100 l o g ( 100 ) \frac{x}{log(x)}= \frac{100}{log(100)}

x = 100 x=100

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Good work. Can you explain why there's only one solution?

m u l t i p l y b y 2 2 multiply by \frac{2}{2}

Majed Musleh - 6 years ago
Ramiel To-ong
Jun 8, 2015

only 100 satisfies for the given equation

0 Helpful 0 Interesting 0 Brilliant 1 Confused

What and why only 100?

. . - 3 months, 3 weeks ago

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