Logarithmic and exponential functions quiz: O-Level Additional Mathematics (SEAB 4049) quiz

$\log_a(x + y)$

$\log_a(xy)$

$\log_a\left(\dfrac{x}{y}\right)$

$\log_a x \times \log_a y$

$n + \log_a x$

$(\log_a x)^n$

$n\log_a x$

$\log_a(nx)$

$0$

undefined

$a$

$1$

$\dfrac{\log_b x}{\log_b a}$

$\log_b x \times \log_b a$

$\dfrac{\log_b a}{\log_b x}$

$\log_b x - \log_b a$

$(0, 1)$

$(1, 0)$

$(0, 0)$

$(1, 1)$

$y = 0$

$y = x$

$x = 0$

$y = -x$

$x = 2$

$x = 8$

$x = 4$

$x = 5$

Add $\log$ to one side only

Differentiate both sides

Square both sides

Take logarithms of both sides

Because a logarithm is only defined for a positive argument

To make the answer a whole number

Because logarithms can be negative

To round to 3 significant figures

$x = 12$

$x = 81$

$x = 64$

$x = 7$

$y$ against $x$

$y$ against $\lg x$

$\lg y$ against $\lg x$

$\lg y$ against $x$

$\lg a$

$\lg n$

$a$

$n$

$3$

$4$

$2$

$\dfrac{1}{3}$