An algebra problem by abhishek anand

Algebra Level 1

If $\LARGE \displaystyle x^{x^4}=4$ then what is the value of $x$

4

2^{0.56}

2^{0.5}

2

2 solutions

Vaibhav Prasad
Mar 24, 2015

$\huge {{ \sqrt { 2 } }^{ { \sqrt { 2 } }^{ 4 } }\\ { \sqrt { 2 } }^{ { { 2 }^{ \frac { 1 }{ 2 } \times 4 } } }\\ { \sqrt { 2 } }^{ { 2 }^{ 2 } }\\ { \sqrt { 2 } }^{ 4 }\\ { 2 }^{ \frac { 1 }{ 2 } \times 4 }\\ { 2 }^{ 2 }\\ \boxed { 4 }}$

this is a hit and trial method. how can you take x as 2^.5 directly

abhishek anand - 6 years, 2 months ago

1) Because you gave options

2) It was either this or 2^.25

Bhai thoda dimag laga na !!!! iske alawa kya ho sakta hai ???

Vaibhav Prasad - 6 years, 2 months ago

correct !!but that was not the real solution which you gave

abhishek anand - 6 years, 2 months ago

@Abhishek Anand –

Vaibhav Prasad - 6 years, 2 months ago

@Vaibhav Prasad – Bwahaha.. Lol xD

Hrishik Mukherjee - 6 years, 2 months ago

abhishek is right this is not a right solution

ankura sharmi - 6 years, 2 months ago

Chenyang Sun
Mar 26, 2015

See the equation as 4=x^x^4 instead. Substitute x^x^4 for 4 indefinitely gives you x^x^x^x^x......=4, so substitute 4 for x^x^x....gives you x^4=4, or x=√2. Note: The substitute is possible because both x^x^4 and x^x^x^x... are continuous on the positive.

abhishek anand .I had seen all your problems are just copied from india pre rmo 2014 mumbai region question paper.

Saurav Sah - 6 years, 2 months ago

An algebra problem by abhishek anand

2 solutions

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