Question

Suppose the functions L and K are defined by L(x)=log2 x/4 ; K(x)= log4 x/8 respectively. Find the coordinates of the point(s) of intersection of the graphs of L and K with each other

Answer 1

use change of base on the second eqn , get it to base 2

Answer 2

then compare coeffiecents

Answer 3

when you change the base you will get a factor of (1/2) or something, which you will will need to take inside the logarithm , and make it a root

Answer 4

The two graphs intersect when \(\log_2({\frac{x}{4}})=\log_4({\frac{x}{8}})\). Using change of base rule, we get \(\log_2({\frac{x}{4}})=\frac{\log_2({\frac{x}{8}})}{2} \implies (\frac{x}{4})^2=\frac{x}{8}\). Solving this quadratic equation we get:
\[{x^2 \over 16}={x \over 8} \implies x^2-2x=0 \implies x(x-2)=0\] So, we have \(x=2\). We rejected \(x=0\) since both functions are undefined at \(x=0\).

Answer 5

Therefore the intersection point is \((2,-1)\).

Answer 6

Thank you :)