I was thinking about different log laws and stuff but i don't know how to get to that. It was on a past paper im pratising on at the moment.
If anyone can help, il really appreciate it.
Hello chinkmeista
$\displaystyle \log_ax^{10} - 2\log_a\left(\frac{x^3}{4}\right)$
$\displaystyle = \log_ax^{10} -\log_a\left(\frac{x^3}{4}\right)^2$
$\displaystyle = \log_ax^{10} -\log_a\left(\frac{x^6}{16}\right)$
$\displaystyle = \log_a\left(x^{10}\times\frac{16}{x^6}\right)$
$\displaystyle = \log_a(16x^4)$
$\displaystyle =4\log(2x)$
Grandad
Oh hi, thats fantastic thank you. I kinda understand it, up until like the 3rd step though from:
$\displaystyle = \log_ax^{10} -\log_a\left(\frac{x^6}{16}\right)$
to
$\displaystyle = \log_a\left(x^{10}\times\frac{16}{x^6}\right)$
how did you flip the 16 and x^6 upside down and merge the x^10 together at the same time? could you explain how you did this bit?
Again, thanks a lot.
Hello chinkmeista
$\displaystyle \log a - \log b = \log (a \div b)$, and to divide by a fraction, turn it 'upside down' and multiply.
So $\displaystyle \log_a x - \log_a \left(\frac{y}{z} \right) = \log \left(x \times \frac{z}{y} \right )$.
Can you see it OK now?
Grandad