Logarithms' challenger #3

Algebra Level 2

$\large{x^{\dfrac{\log x+5}{3}}=10^{5+\log x}}$

Find the value of $x$ satisfying the below equation above where $x$ is an integer.

This problem is a part of this set .

The answer is 1000.

4 solutions

Akhil Bansal
Oct 10, 2015

Its a one line question,
Suppose $\log_{10} x + 5 = k$

$\Rightarrow \large x^{k/3} = 10^k \Rightarrow \color{#3D99F6}{\boxed{x = 1000}}$

Same method

I think I need not post the same solution again.(just joking)

Rama Devi - 5 years, 2 months ago

Raj Rajput
Oct 10, 2015

@rohit udaiwal edit your problem as x is an integer :)

RAJ RAJPUT - 5 years, 8 months ago

Thanks for notifying:P

Rohit Udaiwal - 5 years, 8 months ago

Can you explain me this one?

Abhiram Rao - 5 years, 2 months ago

@Abhiram Rao – Which step(s) is troubling you?I would love to help you :D Also, you may want to read this .

Rohit Udaiwal - 5 years, 2 months ago

@Rohit Udaiwal – Done! Thanks :D

Abhiram Rao - 5 years, 2 months ago

@Abhiram Rao – Great!It's awesome to see a genius 8 grader like you solving such problems!BTW do you like the set?It was my first ever set so I'm always kinda excited about it:P

Rohit Udaiwal - 5 years, 2 months ago

@Rohit Udaiwal – Interesting :D

Abhiram Rao - 5 years, 2 months ago

Aakash Khandelwal
Oct 13, 2015

Take log on both sides and approach a quadratic .

Sai Aryanreddy
Oct 11, 2015

Ur in DSNR?

Abhiram Rao - 5 years, 2 months ago

Logarithms' challenger #3

This problem is a part of this set .

The answer is 1000.

4 solutions

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