perplexus.info :: Just Math : Irrational powered equation

Irrational powered equation (Posted on 2023-07-30)

Find all real solutions to the equation

(2+√3)^x+1=(2(2+√3))^x

No Solution Yet Submitted by Danish Ahmed Khan

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computer solution

| Comment 1 of 3

syms x

s=solve(@(x)(2+sqrt(3))^x+1==(2*(2+sqrt(3)))^x,x)

fplot(@(x)(2+sqrt(3))^x+1);

hold on

fplot(@(x)(2*(2+sqrt(3)))^x)

grid

s =

0.562446450284434389721623002976895 approximately

The plot does cross at a point consistent with this result.

At this value of x, both sides evaluate to 3.097441553851361281265557 approximately.

Posted by Charlie on 2023-07-30 16:30:32

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