{"status": "success", "data": {"description_md": "Given that $2^{2004}$ is a $604$-digit number whose first digit is $1$, how many elements of the set $S = \\{2^0,2^1,2^2,\\ldots ,2^{2003}\\}$ have a first digit of $4$? \n\n$\\mathrm{(A)}\\ 194\\qquad\\mathrm{(B)}\\ 195\\qquad\\mathrm{(C)}\\ 196\\qquad\\mathrm{(D)}\\ 197\\qquad\\mathrm{(E)}\\ 198$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Given that <span class=\"katex--inline\">2^{2004}</span> is a <span class=\"katex--inline\">604</span>-digit number whose first digit is <span class=\"katex--inline\">1</span>, how many elements of the set <span class=\"katex--inline\">S = \\{2^0,2^1,2^2,\\ldots ,2^{2003}\\}</span> have a first digit of <span class=\"katex--inline\">4</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 194\\qquad\\mathrm{(B)}\\ 195\\qquad\\mathrm{(C)}\\ 196\\qquad\\mathrm{(D)}\\ 197\\qquad\\mathrm{(E)}\\ 198</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2004 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/04_amc12B_p24"}}