Question

If you're good at logarithms please help me with question j on the bottom

Answer 1

Answer:

$\log _x\left(6\right)$

$\frac{\text{log}(6)}{\text{log}(x)} =\frac{\text{log}(3)}{\text{log}x)}+\frac{\text{log}(3)}{\text{log}(x)}=\frac{1.5}{\text{log}(x)}+\frac{1.5}{\text{log}(x)}=\frac{3}{\log _{10}\left(x\right)}$

Answer 2

Step-by-step explanation:

$a) \\ log_{x}(15) \\ = log_{x}(3 \times 5) \\ = log_{x}3 + log_{x}5 \\ = 1.5 + 1.8 \\ = 3.3$

$b) \\ log_{x}(2) \\ = log_{x}(\frac{10}{5}) \\ = log_{x}10 - log_{x}5 \\ = 3 - 1.8\\= 1.2$

$e) \\ log_{x}(150) \\ = log_{x}(3 \times 5\times 10) \\ = log_{x}3 + log_{x}5+ log_{x}10 \\ = 1.5 + 1.8 + 3\\ = 6.3$

$f) \\ log_{x}(250) \\ = log_{x}( 5^2 \times 10) \\ = log_{x}5^2 + log_{x}10 \\ = 2log_{x}5 + log_{x}10 \\ = 2\times 1.8 + 3\\ = 3.6 + 3\\= 6.6$