Question

if 3^x+3 = 1/(81)^x-2, find the value of (3x)^2x

Answer 1

S O L U T I O N :

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$:\implies\sf{3^{x+3}=\bigg(\dfrac{1}{81}\bigg)^{x-2}}\\\\\\:\implies\sf{3^{x+3}=\bigg(\dfrac{1}{3^4}\bigg)^{x-2}}\\\\\\:\implies\sf{3^{x+3}=\bigg(\dfrac{1}{3}\bigg)^{4x-8}}\\\\\\:\implies\sf{3^{x+3}=3^{-4x+8}}\\\\\\:\implies\sf{x+3=-4x+8}\\\\\\:\implies\sf{x+4x=8-3}\\\\\\:\implies\sf{5x=5}\\\\\\:\implies\sf{x=\dfrac{5}{5}}\\\\\\:\implies\underline{\boxed{\frak{\textcolor{lavender}{x=1}}}}\;\bigstar$

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T H E R E F O R E :

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$:\implies\sf{(3x)^{2x}}\\\\\\:\implies\sf{(3(1))^{2(1)}}\\\\\\:\implies\sf{3^2}\\\\\\:\implies{\textsf{\textbf{9}}}$

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