// Numbas version: exam_results_page_options
{"name": "Simon's copy of 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": [{"tags": [], "advice": "<p><strong>(a)</strong></p>\n<p><strong></strong>$2^{\\var{num11}x-\\var{num12}} = \\var{nn1}^{x+\\var{num13}}$</p>\n<p>$2^{\\var{num11}x-\\var{num12}}= (2^\\var{log({nn1},2)})^{x+\\var{num13}}$</p>\n<p>$2^{\\var{num11}x-\\var{num12}}= 2^{\\var{log({nn1},2)}(x+\\var{num13})}$</p>\n<p>$\\implies&nbsp;\\var{num11}x-\\var{num12} =&nbsp;\\var{log({nn1},2)}(x+\\var{num13})$</p>\n<p>$\\implies&nbsp;\\var{num11}x-\\var{num12} =&nbsp;\\var{log({nn1},2)}x +\\var{log({nn1},2)*num13}$</p>\n<p>$\\implies&nbsp;\\var{num11-log({nn1},2)}x =&nbsp;\\var{num12+log({nn1},2)*num13}$</p>\n<p>$\\implies x =&nbsp;\\var{(num12+log({nn1},2)*num13)/(num11-log({nn1},2))}$</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p><strong></strong></p>\n<p>$(3^\\var{log({nn21},3)})^{x-\\var{num21}} = (3^\\var{log({nn22},3)})^{\\var{num22} - x}$</p>\n<p>$3^{\\var{log({nn21},3)}({x-\\var{num21}})} =3^{\\var{log({nn22},3)}({\\var{num22} - x})}$</p>\n<p>$\\implies&nbsp;\\var{log({nn21},3)}({x-\\var{num21}}) ={\\var{log({nn22},3)}({\\var{num22} - x})} $</p>\n<p>$\\implies&nbsp;\\var{log({nn21},3)} x-\\var{log({nn21},3)*num21} =\\var{log({nn22},3)*{num22}} -\\var{log({nn22},3)} x $</p>\n<p>$\\implies&nbsp;\\var{log({nn21},3)+log({nn22},3)} x =\\var{log({nn22},3)*{num22} +log({nn21},3)*num21} $</p>\n<p>$\\implies&nbsp; x =\\var{(log({nn22},3)*{num22}+log({nn21},3)*num21)/(log({nn21},3)+log({nn22},3))}&nbsp;$</p>\n<p></p>\n<p></p>\n<p><strong>(c)</strong></p>\n<p>$\\var{nn31}^{\\var{num31}x+\\var{num32}} = \\frac{1}{\\var{nn32}}$</p>\n<p>$(2^\\var{log(nn31,2)})^{\\var{num31}x+\\var{num32}}= \\var{2}^{-\\var{log({nn32},2)}}$</p>\n<p>$2^{\\var{log(nn31,2)}({\\var{num31}x+\\var{num32}})}= \\var{2}^{-\\var{log({nn32},2)}}$</p>\n<p>$\\implies \\var{log(nn31,2)}({\\var{num31}x+\\var{num32}})= -\\var{log({nn32},2)}$</p>\n<p>$\\implies&nbsp; \\var{log(nn31,2)*{num31}}x+\\var{log(nn31,2)*num32}=-\\var{log({nn32},2)}$</p>\n<p>$\\implies x=\\frac{-\\var{log({nn32},2)}-\\var{log(nn31,2)*num32}}{\\var{log(nn31,2)*{num31}}}=\\var{(-log({nn32},2)-log(nn31,2)*num32)/(log(nn31,2)*{num31})}$</p>\n<p></p>\n<p></p>\n<p><strong>(d)</strong></p>\n<p>$\\var{nn41}^{\\var{num41}x-\\var{num42}} = \\var{nn42}^{\\var{num43} - x}$</p>\n<p>$(5^\\var{log({nn41},5)})^{\\var{num41}x-\\var{num42}} = (5^\\var{log({nn42},5)})^{\\var{num43} - x}$</p>\n<p>$5^{\\var{log({nn41},5)}({\\var{num41}x-\\var{num42}})} =5^{\\var{log({nn42},5)}({\\var{num43} - x})}$</p>\n<p>$\\implies&nbsp;\\var{log({nn41},5)}({\\var{num41}x-\\var{num42}}) ={\\var{log({nn42},5)}({\\var{num43} - x})} $</p>\n<p>$\\implies&nbsp;\\var{log({nn41},5)*num41} x-\\var{log({nn41},5)*num42} =\\var{log({nn42},5)*{num43}} -\\var{log({nn42},5)} x $</p>\n<p>$\\implies&nbsp;\\var{log({nn41},5)*num41+log({nn42},5)} x =\\var{log({nn42},5)*{num43} +log({nn41},5)*num42} $</p>\n<p>$\\implies&nbsp; x =\\var{(log({nn42},5)*{num43}+log({nn41},5)*num42)/(log({nn41},5)*num41+log({nn42},5))}&nbsp;$</p>\n<p></p>", "name": "Simon's copy of Q3 Indices; Solve for x", "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "ans1<100 and ans2<100 and ans3<100 and ans4<100", "maxRuns": 100}, "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"], "variable_groups": [], "variables": {"p42": {"group": "Ungrouped variables", "definition": "random(2..3 except p41)", "description": "", "name": "p42", "templateType": 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"maxValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "allowFractions": true, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "unitTests": [], "customMarkingAlgorithm": "", "minValue": "{ans1}", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain"}], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>$2^{\\var{num11}x-\\var{num12}} = \\var{nn1}^{x+\\var{num13}}$</p>\n<p>$x =$&nbsp;[[0]]</p>", "scripts": {}}, {"type": "gapfill", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "gaps": [{"type": "numberentry", "mustBeReduced": false, "maxValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "allowFractions": true, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "unitTests": [], "customMarkingAlgorithm": "", "minValue": "{ans2}", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain"}], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>$\\var{nn21}^{x-\\var{num21}} = \\var{nn22}^{\\var{num22} - x}$</p>\n<p>$x=$&nbsp;[[0]]</p>", "scripts": {}}, {"type": "gapfill", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "gaps": [{"type": "numberentry", "mustBeReduced": false, "maxValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "allowFractions": true, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "unitTests": [], "customMarkingAlgorithm": "", "minValue": "{ans3}", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain"}], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>$\\var{nn31}^{\\var{num31}x+\\var{num32}} = \\frac{1}{\\var{nn32}}$</p>\n<p>$x&nbsp;=$&nbsp;[[0]]</p>", "scripts": {}}, {"type": "gapfill", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "gaps": [{"type": "numberentry", "mustBeReduced": false, "maxValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "allowFractions": true, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "unitTests": [], "customMarkingAlgorithm": "", "minValue": "{ans4}", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain"}], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>$\\var{nn41}^{\\var{num41}x-\\var{num42}} = \\var{nn42}^{\\var{num43} - x}$</p>\n<p>$x&nbsp;=$&nbsp;[[0]]</p>", "scripts": {}}], "extensions": [], "statement": "<p>Solve for $x$ in each of the following:</p>\n<p><em>Enter answer as a whole number or fraction</em></p>", "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Indices</p>\n<p>rebelmaths</p>"}, "functions": {}, "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": 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