// Numbas version: exam_results_page_options
{"name": "Q3 Indices; Solve for x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["num11", "num12", "num13", "nn1", "p1", "ans1", "num21", "num22", "p21", "p22", "nn21", "nn22", "ans2", "p31", "p32", "num31", "num32", "ans3", "p41", "p42", "num41", "num42", "num43", "ans4", "nn31", "nn32", "nn41", "nn42"], "name": "Q3 Indices; Solve for x", "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>i) $2^{4x-3} = 4^{x+1}$</p>\n<p>$2^{4x-3} = 2^{2x+2}$</p>\n<p>$4x-3 = 2x+2$</p>\n<p>$4x-2x = 3+2$</p>\n<p>$x = \\frac{5}{2}$</p>\n<p></p>\n<p>ii) $9^{x-4} = 27^{2-x}$</p>\n<p>$3^{2x-8} = 3^{6-3x}$</p>\n<p>$2x-8 = 6-3x$</p>\n<p>$2x+3x = 6+8$</p>\n<p>$x = \\frac{14}{5}$</p>\n<p></p>\n<p>iii) $2^{2x+3} = \\frac{1}{4}$</p>\n<p>$2^{2x+3} = 2^{-2}$</p>\n<p>$2x+3 = -2$</p>\n<p>$2x = -2-3$</p>\n<p>$x = \\frac{-5}{2}$</p>\n<p></p>\n<p>iv) $25^{2x-3} = 5^{4-x}$</p>\n<p>$5^{4x-6} = 5^{4-x}$</p>\n<p>$4x-6 =&nbsp;4-x$</p>\n<p>$4x+x = 4+6$</p>\n<p>$x = 2$</p>", "rulesets": {}, "parts": [{"prompt": "<p>$2^{\\var{num11}x-\\var{num12}} = \\var{nn1}^{x+\\var{num13}}$</p>\n<p>x =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{nn21}^{x-\\var{num21}} = \\var{nn22}^{\\var{num22} - x}$</p>\n<p>x=&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{nn31}^{\\var{num31}x+\\var{num32}} = \\frac{1}{\\var{nn32}}$</p>\n<p>x&nbsp;=&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{nn41}^{\\var{num41}x-\\var{num42}} = \\var{nn42}^{\\var{num43} - x}$</p>\n<p>x&nbsp;=&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve for x in each of the following:</p>\n<p><em>Enter answer as whole number or fraction</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "(num12+num13*p1)/(num11-p1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(num22*p22+num21*p21)/(p21+p22)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "((p32*-1)-num32*p31)/(p31*num31)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "((p42*num43)+num42*p41)/((p41*num41)+p42)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "p21": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p21", "description": ""}, "p22": {"definition": "random(1..3 except p21)", "templateType": "anything", "group": "Ungrouped variables", "name": "p22", "description": ""}, "p42": {"definition": "random(1..3 except p41)", "templateType": "anything", "group": "Ungrouped variables", "name": "p42", "description": ""}, "p41": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p41", "description": ""}, "nn22": {"definition": "3^(p22)", "templateType": "anything", "group": "Ungrouped variables", "name": "nn22", "description": ""}, "nn21": {"definition": "3^(p21)", "templateType": "anything", "group": "Ungrouped variables", "name": "nn21", "description": ""}, "num22": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num21": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num41": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num41", "description": ""}, "num43": {"definition": "random(3..6 except [num41,num42])", "templateType": "anything", "group": "Ungrouped variables", "name": "num43", "description": ""}, "num42": {"definition": "random(3..6 except num41)", "templateType": "anything", "group": "Ungrouped variables", "name": "num42", "description": ""}, "nn41": {"definition": "5^p41", "templateType": "anything", "group": "Ungrouped variables", "name": "nn41", "description": ""}, "nn42": {"definition": "5^p42", "templateType": "anything", "group": "Ungrouped variables", "name": "nn42", "description": ""}, "p32": {"definition": "random(1..3 except p31)", "templateType": "anything", "group": "Ungrouped variables", "name": "p32", "description": ""}, "p31": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p31", "description": ""}, "nn1": {"definition": "2^(p1)", "templateType": "anything", "group": "Ungrouped variables", "name": "nn1", "description": ""}, "p1": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "nn31": {"definition": "2^p31", "templateType": "anything", "group": "Ungrouped variables", "name": "nn31", "description": ""}, "nn32": {"definition": "2^p32", "templateType": "anything", "group": "Ungrouped variables", "name": "nn32", "description": ""}, "num12": {"definition": "random(3..5 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num11": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num31": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num31", "description": ""}, "num32": {"definition": "random(3..6 except num31)", "templateType": "anything", "group": "Ungrouped variables", "name": "num32", "description": ""}}, "metadata": {"description": "<p>Indices</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}