perplexus.info :: Just Math : Only one real answer

Only one real answer (Posted on 2023-09-01)

8^x+2^x=130

Provide the solution, x must be a real number.

Source: Mexican Math. Olymp.

See The Solution Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Solution

| Comment 1 of 2

Substitute y = 2^x

y^3 + y = 130

125 + 5 = 130

y = 5

2^x = 5

x = ln(5) / ln(2)

x ~ 2.321928094887362

Since LHS is an increasing function and RHS is constant, there is only one real answer

Posted by Larry on 2023-09-01 08:39:47

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