and logarithms Flashcards","topicId":"7af838ce-1ad8-44ab-bc02-76ccd350f501","topicSlug":"exponentials-and-logarithms-5","cards":[{"id":"6c2a11a8-d7b1-4a30-874e-e9cda3f6e795","cardType":"basic","front":"What is the approximate value of $e$?","back":"$e\\approx 2.71828$","points":1,"mcqOptions":null},{"id":"6f153692-021a-4e1f-bd0f-6a83f9553245","cardType":"basic","front":"What are the domain and range of $y=e^x$?","back":"

Domain: all real numbers
Range: $y>0$

","points":3,"mcqOptions":null},{"id":"ada74408-3e86-453f-8c2c-ae983155af0c","cardType":"basic","front":"What is the horizontal asymptote of $y=e^x$?","back":"$y=0$","points":1,"mcqOptions":null},{"id":"189f7833-54d3-4153-b71c-01648074d07d","cardType":"basic","front":"What restriction applies to the input of $\\ln x$?","back":"It must be strictly positive: $x>0$.","points":1,"mcqOptions":null},{"id":"2788e983-d7ed-4705-919e-af20c31ddac9","cardType":"cloze","front":"The inverse relationships are $\\text{[...]}$ and $e^{\\ln x}=x$, where $x>0$.","back":"The inverse relationships are $\\boxed{\\ln(e^x)=x}$ and $e^{\\ln x}=x$, where $x>0$.","points":null,"mcqOptions":null},{"id":"b5f7c8fa-fa1d-4a89-aeb2-f03b4cc482fe","cardType":"cloze","front":"The inverse relationships are $\\ln(e^x)=x$ and [ ].","back":"The inverse relationships are $\\ln(e^x)=x$ and $e^{\\ln x}=x$, where $x>0$.","points":null,"mcqOptions":null},{"id":"39dffbc2-7f6a-4c79-bcb0-624783cdf9cb","cardType":"basic","front":"Evaluate $\\ln(e^5)$.","back":"$5$","points":1,"mcqOptions":null},{"id":"7fc2bada-13e8-43bd-bfa0-e80ea8dec770","cardType":"basic","front":"Evaluate $\\ln\\left(\\frac{1}{e^2}\\right)$.","back":"$-2$","points":1,"mcqOptions":null},{"id":"30a9700e-c1fe-4ce8-a98b-f501ebcdf4f8","cardType":"basic","front":"What are the domain and range of $y=\\ln x$?","back":"

Domain: $x>0$
Range: all real numbers

","points":3,"mcqOptions":null},{"id":"0755bf3e-5b0b-4df2-b17f-16762f5f112b","cardType":"basic","front":"What is the vertical asymptote of $y=\\ln x$?","back":"$x=0$","points":1,"mcqOptions":null},{"id":"5c70fa56-0346-4a70-8b98-a9db25b3398f","cardType":"basic","front":"What is the sign of $\\ln x$ when $0$\\ln x<0$","points":1,"mcqOptions":null},{"id":"f7cfa743-baf6-45de-8255-f378da463232","cardType":"basic","front":"How are the graphs of $y=e^x$ and $y=\\ln x$ related?","back":"They are reflections in $y=x$.","points":2,"mcqOptions":null},{"id":"842750c7-e952-40dc-99dc-1ebb4a957e20","cardType":"basic","front":"Which point on $y=\\ln x$ corresponds to $(1,e)$ on $y=e^x$?","back":"$(e,1)$","points":1,"mcqOptions":null},{"id":"1c75530b-3a1f-4cb3-8884-c523be30abb2","cardType":"cloze","front":"For positive $a$ and $b$, the product law is $\\text{[...]}$ and the quotient law is $\\ln\\left(\\frac{a}{b}\\right)=\\ln a-\\ln b$.","back":"For positive $a$ and $b$, the product law is $\\boxed{\\ln(ab)=\\ln a+\\ln b}$ and the quotient law is $\\ln\\left(\\frac{a}{b}\\right)=\\ln a-\\ln b$.","points":null,"mcqOptions":null},{"id":"d530be5a-5eac-4592-b7cf-a47f855cb9e0","cardType":"cloze","front":"For positive $a$ and $b$, the product law is $\\ln(ab)=\\ln a+\\ln b$ and the quotient law is $\\text{[...]}$.","back":"For positive $a$ and $b$, the product law is $\\ln(ab)=\\ln a+\\ln b$ and the quotient law is $\\boxed{\\ln\\left(\\frac{a}{b}\\right)=\\ln a-\\ln b}$.","points":null,"mcqOptions":null},{"id":"e763e860-2911-437e-87b5-c3ca80bab9b6","cardType":"cloze","front":"For $a>0$, the power law is $\\text{[...]}$.","back":"For $a>0$, the power law is $\\boxed{\\ln(a^n)=n\\ln a}$.","points":null,"mcqOptions":null},{"id":"3b363332-a60a-4cc2-85f5-d21aef9af2c6","cardType":"basic","front":"Why is $\\ln(a+b)=\\ln a+\\ln b$ generally i

1.5.4 Exponentials and logarithms Flashcards

1.5.4 Exponentials and logarithms Flashcards