Question

$4^{2x-1}-{16}^{x-1}=348$ find x

Answer 1

$4^{2x-1}-{16}^{x-1}=348$

$\Rightarrow 4^{2x-1}-4^{2(x-1)}=384$

$\Rightarrow 4^{2x-1}-4^{2x-2}=384$

$\Rightarrow 4^{2x-1}[1-1/4]=384$

$\Rightarrow 4^{2x-1}\left(\frac{3}{4}\right)=384$

$\Rightarrow 4^{2x-1}=\frac{384\times 4}{3}$

$\Rightarrow 4^{2x-1}=128\times 4$

$\Rightarrow 4^{2x-1}=512$

$\Rightarrow 4^{2x-1}=2^9$

$\Rightarrow 2^{2(2x-1)}=2^9$

$\Rightarrow 4x-2=9$ [Comparing exponents]

$\Rightarrow 4x=11$

$\Rightarrow x=\frac{11}{4}$