Question

Solve for x : (i)$2^{x+1}=4^{x-3}\\ (ii)2^{5x+3}=8^{x+3}$

Answer 1

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Answer:

i) x=7    ii) x=3

Step-by-step explanation:

$Answers.\\i) 2^{x+1} =4^{x-3}\\=>4^{x-3} can. be. written. as.2^{2}^{(x-3)} \\=>2^{x+1} = 2^{2}^{(x-3)}\\As.the.bases.are.same.so,we.can.abolish.them.\\Therefore,x+1=2(x-3)\\=>x+1=2x-6\\=>1+6=2x-x\\Therefore,x=7\\\\ii) 2^{5x+3}=8^{x+3}\\=>8^{x+3}can.be.written.as.2^{3(x+3)}\\=> 2^{5x+3}=2^{3(x+3)}\\=>As.bases.are.same.we.can.exclude.them.\\Therefore,5x+3={3(x+3)}\\=>5x+3=3x+9\\=>2x=6\\Therefore,x=3$Thank you.....

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