See Also
Flashcards
$$y = a^x \ y = a^{-x}$$ 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??
$$ 1 $$
$$\log_a b = c$$ 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
Why does $\log_a x$ always cut the $x$-axis at $1$??
Because $a^0$ always equals $1$.
Why does the graph of $\log_a x$ get steeper the smaller value of $a$??
Because you have the raise $a$ to a higher power to get the same result.
What is $10^{\log_{10} x}$??
$$ x $$
For what value of $a^x$ does the ratio between the gradient a point and the value of the point equal $1$??
$$ e $$
$$\frac{dy}{dx} \div y : 2^x \to 0.7, 3^x \to 1.1$$ What value base do you need to raise to the power of $x$ for it to equal $1$??
$$ e $$
2021-05-13
What’s the general exponential model for a population $p$ with a initial population $a$, a “growth rate” $b$ and a time $t$??
$$ p = ab^t $$
What do you get if you simlify the $\log_10$ of both sides of $p = ab^t$??
$$ \log_{10} p = t\log_{10} b + \log_{10} a $$
What should you plot for a time $t$ and a poopulation size $p$ to see if the population grows exponentially??
$t$ against $\log_{10}(p)$.
What is the gradient of a $t$ against $\log_10(p)$ graph equal to??
$$ \log_{10}(b) $$
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
$$ (2x+1)\ln(3) = (3x)\ln(3) $$
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Metadata
date: 2021-02-01 09:59
tags:
- '@?maths'
- '@?public'
- '@?further-maths'
title: Maths - Exponentials