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false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "John Wick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3326/"}], "variable_groups": [], "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "preamble": {"css": "", "js": ""}, "advice": "<p>You will require the laws of logarithms:</p>\n<p>$\\log{a} + \\log{b} = \\log{ab}$</p>\n<p>$\\log{a} - \\log{b} = \\log{\\frac{a}{b}}$</p>\n<p>$\\log{a^n} = n\\log{a}$</p>\n<p></p>\n<p><strong>(a)</strong></p>\n<p>$\\log{\\var{a1}} + \\log{\\var{a2}} = \\log({\\var{a1}\\times\\var{a2}})=\\log{\\var{a1*a2}}$</p>\n<p><strong>(b)</strong></p>\n<p>$\\log{\\var{b1}} + \\log{\\var{b2}} =&nbsp;\\log({\\var{b1}\\times\\var{b2}})=\\log{\\var{b1*b2}}$</p>\n<p><strong>(c)</strong></p>\n<p>$\\log{\\var{c3}} - \\log{\\var{c2}} =&nbsp;\\log({\\var{c3}\\div\\var{c2}})=\\log{\\var{c3/c2}}$</p>\n<p><strong>(d)</strong></p>\n<p>$\\log{\\var{e1}} + \\log{\\var{e2}}+ \\log{\\var{e3}} =&nbsp;\\log({\\var{e1}\\times\\var{e2}\\times\\var{e3}})=\\log{\\var{e1*e2*e3}}$</p>\n<p><strong>(e)</strong></p>\n<p>$\\log{\\var{f1}} + \\log{\\var{f3}} - \\log{\\var{f5}} = &nbsp;\\log({\\var{f1}\\times\\var{f3}\\div\\var{f5}})=\\log{\\var{f1*f3/f5}}$</p>\n<p><strong>(f)</strong></p>\n<p>$\\var{g1}\\log{\\var{g2}} + \\log{\\var{g3}} - \\log{\\var{g4}}=&nbsp;\\log({\\var{g2}^\\var{g1}\\times\\var{g3}\\div\\var{g4}})=\\log{\\var{g2^g1*g3/g4}}$</p>\n<p><strong>(g)</strong></p>\n<p>$\\frac{1}{2}\\log{\\var{h3}} - \\frac{1}{2}\\log{\\var{h2}}=\\frac{1}{2}(\\log{\\var{h3}} - \\log{\\var{h2}})= \\frac{1}{2}&nbsp;\\log({\\var{h3}\\div\\var{h2}})=\\frac{1}{2}&nbsp;\\log({\\var{h3/h2}})=\\log(\\var{h3/h2}^\\frac{1}{2})=\\log{\\var{(h3/h2)^0.5}}$</p>\n<p><strong>(h)</strong></p>\n<p>$\\log{\\var{i3}}-\\frac{1}{2}\\log{\\var{i4}} = \\log({\\var{i3}\\div\\var{i4}^\\frac{1}{2}})=&nbsp;\\log({\\var{i3}\\div\\var{i4^0.5}})=\\log{\\var{i3 / i4^0.5 }}$</p>\n<p></p>", "variables": {"d2": {"group": "Ungrouped variables", "name": "d2", "description": "", "templateType": "anything", "definition": "random(2..9 except d1)"}, "g1": {"group": "Ungrouped variables", "name": "g1", "description": "", "templateType": "anything", "definition": "random(2..4)"}, "a2": {"group": "Ungrouped variables", "name": "a2", "description": "", "templateType": "anything", "definition": "random(2..9 except a1)"}, "h2": {"group": "Ungrouped variables", "name": "h2", "description": "", "templateType": "anything", "definition": "random([2,3,5,7,8,10])"}, "i1": {"group": "Ungrouped variables", "name": "i1", 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variables", "name": "c2", "description": "", "templateType": "anything", "definition": "random(2..9 except c1)"}, "a1": {"group": "Ungrouped variables", "name": "a1", "description": "", "templateType": "anything", "definition": "random(2..9)"}, "h1": {"group": "Ungrouped variables", "name": "h1", "description": "", "templateType": "anything", "definition": "random([4,9,16,25])"}, "i4": {"group": "Ungrouped variables", "name": "i4", "description": "", "templateType": "anything", "definition": "i2^2"}, "f3": {"group": "Ungrouped variables", "name": "f3", "description": "", "templateType": "anything", "definition": "f1*f2"}, "c3": {"group": "Ungrouped variables", "name": "c3", "description": "", "templateType": "anything", "definition": "c1*c2"}, "f5": {"group": "Ungrouped variables", "name": "f5", "description": "", "templateType": "anything", "definition": "f1^2"}, "d1": {"group": "Ungrouped variables", "name": "d1", "description": "", "templateType": "anything", "definition": "random(2..19)"}, "g2": {"group": "Ungrouped variables", "name": "g2", "description": "", "templateType": "anything", "definition": "random(2..9 except g1)"}, "g3": {"group": "Ungrouped variables", "name": "g3", "description": "", "templateType": "anything", "definition": "random(2..9 except g2 except g1)"}, "g4": {"group": "Ungrouped variables", "name": "g4", "description": "", "templateType": "anything", "definition": "g2*g3"}, "h3": {"group": "Ungrouped variables", "name": "h3", "description": "", "templateType": "anything", "definition": "h1*h2"}, "f2": {"group": "Ungrouped variables", "name": "f2", "description": "", "templateType": "anything", "definition": "random(3..5 except f1)"}, "b2": {"group": "Ungrouped variables", "name": "b2", "description": "", "templateType": "anything", "definition": "random(2..19 except a1 except a2 except b1)"}, "e3": {"group": "Ungrouped variables", "name": "e3", "description": "", "templateType": "anything", "definition": "random(2..9 except e1 except e2)"}, "e2": {"group": "Ungrouped variables", "name": "e2", "description": "", "templateType": "anything", "definition": "random(2..9 except e1)"}, "b1": {"group": "Ungrouped variables", "name": "b1", "description": "", "templateType": "anything", "definition": "random(2..19 except a2 except a1)"}}, "rulesets": {}, "statement": "<p>You will require the laws of logarithms for these questions:</p>\n<p>$\\log{a} + \\log{b} = \\log{ab}$</p>\n<p>$\\log{a} - \\log{b} = \\log{\\frac{a}{b}}$</p>\n<p>$\\log{a^n} = n\\log{a}$</p>\n<p></p>\n<p></p>\n<p>Express each of the following as a single logarithm.&nbsp;</p>\n<p></p>", "parts": [{"sortAnswers": false, "scripts": {}, "gaps": [{"correctAnswerStyle": "plain", "maxValue": "a1*a2", "scripts": {}, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "type": "numberentry", "mustBeReduced": false, 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