Question

Please help me out with this question.I will be very gratefulप्लीज हेल्प मे आउट ​

Answer 1

${\huge{\red{\sf{Given}}}}\begin{cases}\leadsto \bf{4^{2x-1}-16^{x-1}=384} \\\leadsto \bf{A\: unknown\: variable\:x}\end{cases}$

${\huge{\red{\sf{To\:Find}}}}\begin{cases}\leadsto\bf{The\:value\:of\:x} \end{cases}$

$\huge\red{\underline{\bf{\green{Answer}}}}$

$\sf{\red{Taking\:given\: equation}}$

$\sf{\purple{\longmapsto 4^{2x-1}-16^{x-1}=384}}$

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

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

$\sf{\implies \dfrac{4^{2x}}{4}-\dfrac{4^{2x}}{4^{2}}=384}$

$\sf{\implies \dfrac{4^{2x}}{4}-\dfrac{4^{2x}}{16}=384}$

$\sf{\implies 4^{2x}(\dfrac{1}{4}-\dfrac{1}{16})=384}$

$\sf{\implies 4^{2x}(\dfrac{4-1}{16})=3\times 2^{7}}$

$\sf{\implies 4^{2x}\times \dfrac{3}{16}=3\times 2^{7}}$

$\sf{\implies 4^{2x}=\dfrac{3\times 2^{7}\times 16}{3}}$

$\sf{\implies 4^{2x}=\dfrac{\cancel{3}\times 2^{7}\times 16}{\cancel{3}}}$

$\sf{\implies 2^{4x}=2^{11}}$

$\sf{\pink{\leadsto Ignoring\:the\:bases}}$

$\sf{\implies 4x=11}$

${\underline{\boxed{\red{\bf{\longmapsto x =\dfrac{11}{4}}}}}}$

$\sf{\orange{\therefore The \:value\:of\:x\:is\:\dfrac{11}{4}=2.75}}$

Answer 2

Answer:

11/4 =2.75

I hope it will help you yaar

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