Questions testing rather basic understanding of the index laws.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "(a) Add the powers: $\\var{m} + \\var{n}=\\var{m+n}$ (first index law).
\n(b) Multiply the powers $\\var{m1} \\times \\var{n1}=\\var{m1*n1}$ (second index law).
\n(c) Multiply $\\var{xx}$ and $\\var{y}$ to get $\\var{xx*y}$, with the power unchanged at $\\var{t}$. [This is the only way for the power to be a prime.]
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\nWrite in your answer as e.g., \"{a}^2\" for $\\var{a}^2$
\n[[0]]
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\n\\[(\\var{b}^{\\var{m1}})^{\\var{n1}}\\]
\nWrite your answer as, e.g. \"{b}^2\" for $\\var{b}^2$
\n[[0]]
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\n\n${\\frac{1}{\\var{x5}^\\var{m52}}}$ = [[0]]
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Simplify and write in the form $a \\sqrt{b}$ so that b is not a multiple of a square number.
\nEnter your answer in the form \"a*sqrt(b)\", e.g., write 3*sqrt(2) for $3\\sqrt{2}$)
\n\n$\\sqrt{\\simplify{({xx1}^2)*{kk1}}} $ = [[0]]
\n\n
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Questions testing rather basic understanding of the index laws.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Exponential functions $y = k a^x.$ Growth or decay, x-y intercepts.
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\n
[[0]]
Does it have an x intercept
\n[[1]]
\n\nWhat is the y intercept
\n[[2]]
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Simplify the expressions to fill in the gaps.
", "advice": "We need to use the rule
\n\\[\\log_a(x)+\\log_a(y)=\\log_a(xy)\\text{.}\\]
\nSubstituting in our values for $x$ and $y$ gives
\n\\[\\begin{align}
\\log_a(\\var{x1[1]})+\\log_a(\\var{x1[0]})&=\\log_a(\\var{x1[1]}\\times \\var{x1[0]})\\\\
&=\\log_a(\\var{x1[1]*x1[0]})\\text{.}
\\end{align}\\]
\n
We need to use the rule
\n\\[\\log_a(x)-\\log_a(y)=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}\\]
\nSubstituting in our values for $x$ and $y$ gives
\n\\[\\begin{align}
\\log_a(\\var{x1[4]*y1})-\\log_a(\\var{x1[4]})&=\\log_a(\\var{x1[4]*y1}\\div \\var{x1[4]})\\\\
&=\\log_a(\\var{y1})\\text{.}
\\end{align}\\]
$\\log_a(\\var{x1[1]})+ \\log_a(\\var{x1[0]})=\\log_a($ [[0]]$)$
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\n\\[\\begin{align}
\\log_a(x)+\\log_a(y)&=\\log_a(xy)\\text{,}\\\\
\\log_a(x)-\\log_a(y)&=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}
\\end{align}\\]
$\\log_a(\\var{(x1[4])*y1})-\\log_a(\\var{x1[4]})=\\log_a($ [[0]]$)$
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\n\\[\\begin{align}
\\log_a(x)+\\log_a(y)&=\\log_a(xy)\\text{,}\\\\
\\log_a(x)-\\log_a(y)&=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}
\\end{align}\\]
$ \\log_a (\\var{x1[5]}^\\var{x1[6]}) $ = [[0]]$\\log_a$ ([[1]])
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\n\\[\\begin{align}
p \\log_a(x) &=\\log_a(x^p)\\text{.}\\\\
\\end{align}\\]
Questions testing rather basic understanding of the index laws.
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\n
[[0]]
Does it have a y intercept
\n[[1]]
\nWhat is the x intercept
\n[[2]]
\nThe domain is (use the first box for the sign (>, >=, < or <=), and then write a number in the second box):
\n$x$[[3]][[4]]
\nThe range is (write in the the boxes as: value (or -infinity), sign (< or <=), $y$, sign (< or <=), value (or infinity):
\n[[5]][[6]]$y$[[7]][[8]]
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"preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}, {"name": "Simon James", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18202/"}], "tags": [], "metadata": {"description": "Solve a logarithmic equation
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Solve the following logarithmic equations
\n", "advice": "\\(\\var{a}log(\\var{b}x+\\var{c})=\\var{d}\\)
\nDivide across by \\(\\var{a}\\)
\n\\(log(\\var{b}x+\\var{c})=\\var{d}/\\var{a}=\\simplify{{d}/{a}}\\)
\n\\(\\var{b}x+\\var{c}=10^{\\simplify{{d}/{a}}}\\)
\n\\(\\var{b}x+\\var{c}=\\simplify{10^{{d}/{a}}}\\)
\n\\(\\var{b}x=\\simplify{10^{{d}/{a}}}-\\var{c}\\)
\n\\(\\var{b}x=\\simplify{10^{{d}/{a}}-{c}}\\)
\n\\(x=\\simplify{(10^{{d}/{a}}-{c})/{b}}\\)
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\n\\(y=\\log_\\var{a2} (\\var{b2}x+\\var{c2}))\\)
\ncalculate the value of \\(x\\) that satisfies the equation when \\(y=\\var{d2}\\).
\nInput your answer correct to three decimal places.
\n\\(x = \\) [[0]]
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\n| 1. | \nComplete the questions within 90 minutes and achieve 80% or higher. | \n
| 2. | \nYou can take this self-assessment as many times as you need, until you receive a satisfactory grade (you don't need to achieve 80% when you 'give it a go' the first time) | \n
| 3. | \nUse the \"Print this results summary\" and save as a pdf after you complete your attempt. You will need the printout showing all questions for your module submission. | \n
Congratulations! You have achieved the minimum threshold for this module's self-assessment.
\nUse the \"Print this results summary\" and save your attempt as a pdf. You will need the printout showing all questions for your module submission.
", "threshold": "80"}, {"message": "Unfortunately you have not achieved the minimum score.
\nIf this is your first 'Give it a go' attempt - don't despair! This is exactly why we take our first attempt - to see how we're going and whether we need more practice in order to complete the quest.
\nYou should still use the \"Print this results summary\" option to save a copy of your results as a pdf, which will help with your learning and can also be shared with your tutors so they can help with certain questions.
\n