Question

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Solve the given exponential equations​

Answer 1

√2^x×2=√2^8×2

2^x=2^1x=16

2^2x+1=2^2×2x-1
2x+1=4x-2
3=2x
x=2/3


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Answer 2

Answer :

$( \sqrt{2} ) {}^{x} = 2 {}^{8} \\ \\ ( \sqrt{2} ) {}^{x} = (\sqrt{2}) {}^{2 \times 8} \\ \\ x = 2 \times 8 \\ \\ x = 16$

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$2 {}^{2x + 1} = 4 {}^{2x - 1} \\ \\ 2 {}^{2x + 1} = 2 {}^{2(2x - 1)} \\ \\ 2x + 1 = 4x - 2 \\ \\ 2x - 4x = - 2 - 1 \\ \\ - 2x = - 3 \\ \\ x = \frac{3}{2}$