## Why is this rational? [closed]

### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

Why is ln(`$\pi^{\pi}$`) rational?

-

## 1 Answer

It is not known if it is rational. It's suspected to be transcendental over $\mathbb Q$. It is known that $e^\pi$ is transcendental, but none of $e^e,\pi^e,\pi^\pi$ is known to be irrational or transcendental.

-
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9507079124450684, "perplexity_flag": "middle"}