perplexus.info :: Just Math : Inverse Crossed Linear Power

Inverse Crossed Linear Power (Posted on 2023-10-14)

Determine all possible real x that satisfy this equation:

(1/x)^x = 4^x+1/16

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Find my error

| Comment 2 of 13 |

Take ln of both sides

x ln(1/x) = (x+1/16)ln4

differentiate both sides

ln(1/x) + x*x*(-1)x^(-2) = ln4

ln(1/x) - 1 = ln4

ln(1/x) = ln4 + 1

e to power of both sides

(1/x) = e^(1 + ln4)

(1/x) = 4e

x = 1/(4e) = approximately 0.092

But this is incorrect.

Where's my mistake?

Posted by Larry on 2023-10-14 10:54:27

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