Hi,
Please could anyone help with this problem please? I know the answers from an answer sheet (x=1 and x=ln12/ln4) , but I have no idea how the answers were reached.
Many thanks
4^2x + 48 = 4^(x+2)
$\displaystyle 4^{2x} + 48 = 4^{x+2}$
$\displaystyle 4^{2x} - 4^{x+2} + 48 = 0$
$\displaystyle 4^{2x} - 4^2 \cdot 4^x + 48 = 0$
$\displaystyle (4^x)^2 - 16 \cdot 4^x + 48 = 0$
let $\displaystyle u = 4^x$ ...
$\displaystyle u^2 - 16x + 48 = 0$
solve the quadratic for u by factoring ... then solve for x