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After simplifying, in each case we end up with $\\log_a{f(x)} = b$, so we raise both sides as a power of $a$ to get $a^{\\log_a{f(x)}} = a^b$ which simplifies (by laws of logarithms) to $f(x)=a^b$. We then solve for x accordingly.</p>\n<p>Use of the laws of logarithms is crucial here:</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>", "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "name": "Andrew's copy of Numerical skills Solving Logarithms ", "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "showQuestionGroupNames": false, "type": "question", "tags": [], "parts": [{"marks": 0, "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "gaps": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "minValue": "{a1}", "marks": 1, "correctAnswerFraction": false, "allowFractions": false, "integerAnswer": true, "integerPartialCredit": 0, "maxValue": "{a1}", "variableReplacementStrategy": "originalfirst", "type": "numberentry"}], "prompt": "<p>$\\log_\\var{a2}\\var{a3}+\\log_\\var{a2}x = \\var{a4}$</p>\n<p>$x=$[[0]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"marks": 0, "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "gaps": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "minValue": "{b2}*({b1}^{b3})-{b4}", "marks": 1, "correctAnswerFraction": false, "allowFractions": false, "integerAnswer": true, "integerPartialCredit": 0, "maxValue": "{b2}*({b1}^{b3})-{b4}", "variableReplacementStrategy": "originalfirst", "type": "numberentry"}], "prompt": "<p>$\\log_\\var{b1}(x+\\var{b4})-\\log_\\var{b1}\\var{b2} = \\var{b3}$</p>\n<p>$x=$[[0]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill"}], "extensions": [], "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}]}], "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}