Maths - Exponentials
See Also
Flashcards
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\[y = a^x \\ y = a^{-x}\]What is true about these two graphs?? They are reflections of each other in the $y$-axis.
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\[y = a^x\]What is the $y$-intercept of this graph??
\[1\]#####
\[\log _ a b = c\]If this is true, what is also true??
\[a^c = b\]#####
\[3^x = 9\]What would you do to both sides to make $x$ the subject??
\[\log_3\]#####
\[\log _ a a\]What is this equal to??
\[1\]#####
\[\log _ a 1\]What is this equal to??
\[0\]#####
\[\log _ a \frac{1}{a}\]What is this equal to??
\[-1\]#####
\[\log _ a m + \log _ a n\]How could you rewrite this??
\[\log_a mn\]#####
\[\log _ a mn\]How could you rewrite this??
\[\log_a m + \log_b n\]#####
\[\log _ a m - \log _ b n\]How could you rewrite this??
\[\log_a \left(\frac{m}{n}\right)\]#####
\[\log _ a \left(\frac{m}{n}\right)\]How could you rewrite this??
\[\log_a m - \log_b n\]#####
\[\log _ a x^n\]How could you rewrite this??
\[n \log_a x\]#####
\[n \log _ a x\]How could you rewrite this??
\[\log_a x^n\]#####
\[\log _ a \left(\frac{1}{y}\right)\]How could you rewrite this??
\[-\log_a y\]#####
\[-\log _ a y\]How could you rewrite this??
\[\log_a \left(\frac{1}{y}\right)\]#####
\[2\log a\]How could you rewrite this??
\[\log a^2\]#####
\[\frac{1}{2} \log a\]How could you rewrite this??
\[\log\sqrt{a}\]2021-02-02
\[y = a^x \\ y = a^{-x}\]
What is true about these two graphs?
They are reflections of each other in the $y$-axis.
\[y = a^x\]
What is the $y$-intercept of this graph?
\[\log _ a b = c\]
If this is true, what is also true?
\[3^x = 9\]
What would you do to both sides to make $x$ the subject?
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\[\frac{dy}{dx} \div y : 2^x \to 0.7, 3^x \to 1.1\]What value base do you need to raise to the power of $x$ for it to equal $1$??
\[e\]2021-05-13
\[\log _ a a\]
What is this equal to?
\[\log _ a 1\]
What is this equal to?
\[\log _ a \frac{1}{a}\]
What is this equal to?
\[\log _ a m + \log _ a n\]
How could you rewrite this?
2021-10-12
What is the first stage of solving
\[3^{2x + 1} = 4^{3x}\]?? Taking any $\log$ of both sides.
How can you simplify this
\[\ln(3^{2x+1}) = \ln(4^{3x})\]?? Using the power rule
\[(2x+1)\ln(3) = (3x)\ln(3)\]2022-05-15
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\[\ln(x)^2 - 2\ln(x) + 4\]How can you prove this is never negative?? Complete the square.