and logarithms Flashcards","topicId":"cd76a429-9954-44d6-a423-389d0d56dc2d","topicSlug":"exponentials-and-logarithms-4","cards":[{"id":"2782b142-e7f2-49bf-8724-3d99d9219242","cardType":"basic","front":"In $a^b$, which quantity is the base and which is the exponent?","back":"Base: $a$; exponent: $b$.","points":1,"mcqOptions":null},{"id":"6781594a-fcc9-4d03-9e7e-c20cbf1d706b","cardType":"cloze","front":"A negative exponent gives a reciprocal: $\\text{[...]}$.","back":"A negative exponent gives a reciprocal: $\\boxed{a^{-n}=\\frac{1}{a^n}}$.","points":null,"mcqOptions":null},{"id":"0523d1ca-828d-4b22-a866-e84062ddd18d","cardType":"cloze","front":"A fractional exponent represents a root: $\\text{[...]}$.","back":"A fractional exponent represents a root: $\\boxed{a^{\\frac{1}{n}}=\\sqrt[n]{a}}$.","points":null,"mcqOptions":null},{"id":"aa8b6510-0b49-41b7-bb77-a9e72bc779e5","cardType":"basic","front":"What distinguishes an exponential function such as $f(x)=a^x$?","back":"The variable appears in the exponent.","points":1,"mcqOptions":null},{"id":"423c6a0c-5740-406d-9448-ac45bc18974c","cardType":"basic","front":"Evaluate $4^{-\\frac{3}{2}}$.","back":"$$\\mathbf{\\frac{1}{8}}$","points":2,"mcqOptions":null},{"id":"5f719ec0-27bb-4d5d-8038-374a553d77e4","cardType":"basic","front":"If $f(p)=q$, what does the inverse function do?","back":"It sends $q$ back to $p$: $f^{-1}(q)=p$.","points":1,"mcqOptions":null},{"id":"a21812fa-c695-465f-bc4d-0ee7399cc35e","cardType":"basic","front":"Why is $f^{-1}(x)$ not the same as $\\frac{1}{f(x)}$?","back":"$$f^{-1}$ reverses the function; $\\frac{1}{f(x)}$ takes its reciprocal.","points":2,"mcqOptions":null},{"id":"6e010a00-809d-4929-837f-0dd9ca5a35d8","cardType":"cloze","front":"Exponential and logarithmic forms are equivalent: $\\text{[...]}$.","back":"Exponential and logarithmic forms are equivalent: $\\boxed{a^y=x\\ \\Longleftrightarrow\\ \\log_a x=y}$.","points":null,"mcqOptions":null},{"id":"1b90b6b0-92b9-4520-91c4-338bef1c0446","cardType":"basic","front":"Convert $5^{-2}=\\frac{1}{25}$ to logarithmic form.","back":"$$\\mathbf{\\log_5\\left(\\frac{1}{25}\\right)=-2}$","points":1,"mcqOptions":null},{"id":"c84eeceb-141e-44bd-b118-f9ec6753a4fc","cardType":"basic","front":"Convert $\\log_4 64=3$ to exponential form.","back":"$$\\mathbf{4^3=64}$","points":1,"mcqOptions":null},{"id":"35f9d030-c39e-4d90-875a-bee650c72f43","cardType":"basic","front":"Evaluate $\\log_3 81$.","back":"$$\\mathbf{4}$, because $3^4=81$.","points":1,"mcqOptions":null},{"id":"d026df9a-99bb-4048-bb0b-11ba9e4836df","cardType":"basic","front":"Evaluate $\\log_5\\left(\\frac{1}{125}\\right)$.","back":"$$\\mathbf{-3}$, because $5^{-3}=\\frac{1}{125}$.","points":1,"mcqOptions":null},{"id":"81e89c23-555e-4aa0-95e9-a542336a9b5c","cardType":"basic","front":"In $\\log_a x$, which expression is the argument?","back":"The argument is $x$.","points":1,"mcqOptions":null},{"id":"269c7b0a-4a2f-4221-9773-8c3b6cc8b9be","cardType":"basic","front":"What restrictions make $\\log_a x$ a real logarithm?","back":"

Base: $a>0$ and $a\\neq1$
Argument: $x>0$

","points":3,"mcqOptions":null},{"id":"bbf2d62c-0099-4334-8104-ea648ff22560","cardType":"basic","front":"Why can the base of a logarithm not equal $1$?","back":"Since $1^x=1$ for every $x$, the exponent is not unique.","points":2,"mcqOptions":null},{"id":"8c0ffed9-af78-440b-af3b-5175f8a393e9","cardType":"basic","front":"Why are $\\log_2 0$ and $\\log_2(-8)$ undefined over the reals?","back":"A positive-base exponential always has a positive output.","points":2,"mcqOptions":null},{"id":"ceb4f3e0-7dcd-4a8a-bc89-67426c40fba0","cardType":"cloze","front":"The graphs of $y=a^x$ and $y=\\log_a x$ are reflections in $\\text{[...]}$.","back":"The graphs of $y=a^x$ and $y=\\log_a x$ are reflections in $\\boxed{y=x}$.","points":null,"mcqOptions":null},{"id":"5128d261-9c3d-4b56-add4-b66df6e48c33","c

1.5.3 Exponentials and logarithms Flashcards

1.5.3 Exponentials and logarithms Flashcards