MYP Extended Mathematics Topic 4.1 Logarithms…

True or False: The identity $\frac{\log_a M}{\log_a N} = \log_a (M-N)$ is a valid logarithm law for all .

Using the laws of logarithms, expand the following expression completely (assuming $x > -2$ and $y > 0$ ):

\log_a \sqrt{\frac{(x+2)^2}{y^3}}

If $a = \log_{10} 2$ and $b = \log_{10} 3$ , which of the following represents in terms of and ?

Condense the following expression into a single logarithm with base $b$ :

\frac{1}{3} ( \log_b(x^6) + \log_b(y^3) ) - \log_b(x+1)

For the expression $\log_{x^2-3}(5)$ to be defined for a real number $x$ , which of the following conditions must be satisfied?

$\frac{1}{2}\log_a(x+2) - \frac{3}{2}\log_a y$

$\log_a(x+2) - \frac{3}{2}\log_a y$

$2\log_a(x+2) - 3\log_a y$

$\log_a(x+2) - 3\log_a y$

MYP Extended Mathematics 4.1 Logarithms Questionbank