// Numbas version: finer_feedback_settings {"name": "Solving equations that contain natural log", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "preamble": {"js": "", "css": ""}, "tags": ["rebel", "rebelmaths"], "ungrouped_variables": ["n1", "n2", "n3", "ans1", "n4", "n5", "n6", "n7", "ans2", "n8", "n9", "n10", "ans3"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0, "name": ""}], "advice": "

i) $\\var{n1}\\ln(\\var{n2}x) = \\var{n3}$

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$\\ln(\\var{n2}x) = \\frac{\\var{n3}}{\\var{n1}}$

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Next,

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$\\var{n2}x = e^{\\frac{\\var{n3}}{\\var{n1}}}$

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$x= \\frac{e^{(\\frac{\\var{n3}}{\\var{n1}})} }{\\var{n2}} = \\var{ans1}$

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ii) $\\var{n4}\\ln(\\frac{\\var{n5}x}{\\var{n6}}) = \\var{n7}$

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$\\ln(\\frac{\\var{n5}x}{\\var{n6}}) =\\frac{ \\var{n7}}{\\var{n4}}$

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Next,

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$\\frac{\\var{n5}x}{\\var{n6}}=e^{\\frac{ \\var{n7}}{\\var{n4}}}$

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$x= e^{(\\frac{\\var{n7}}{\\var{n4}})} \\times \\frac{\\var{n6}}{\\var{n5}} = \\var{ans2}$

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iii) $\\var{n8} = \\ln(\\frac{\\var{n9}}{\\var{n10}x})$

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$e^{\\var{n8}}=\\frac{\\var{n9}}{\\var{n10}x}$

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$\\var{n10}xe^{\\var{n8}}=\\var{n9}$

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$x= \\frac{\\var{n9}}{(\\var{n10} \\times e^\\var{n8})} = \\var{ans3}$

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i) $\\var{n1}\\ln(\\var{n2}x) = \\var{n3}$

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$x = $[[0]]

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ii) $\\var{n4}\\ln(\\frac{\\var{n5}x}{\\var{n6}}) = \\var{n7}$

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$x = $[[1]]

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iii) $\\var{n8} = \\ln(\\frac{\\var{n9}}{\\var{n10}x})$

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Give correct to 4 decimal places:

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$x = $[[2]]

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Solve for $x$ in the following, correct to 2 decimal places: 

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Using e to solve equations involving the natural log

", "notes": "

rebelmaths rebel Rebel REBEL

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