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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Answer

Comment 2 of 2 |

Let y=2^x. Then, y^3=8^x. Then, y^3+y=130. Since 5^3+5=125+5=130, then y=5. Then, 2^x=5, so x=log2(5)=2.32...

Posted by Math Man on 2023-09-03 18:08:59

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