Solve for x in the equation 2 x -1-8 x-A- 3B- 1C- -1-13D-

The correct option is D 1/2 nbsp;Given, 2^x+1=8^x 2^x+1=(2^3)^x ⇒ 2^x+1=2^3x (∵ (a^m)^n=a^mn) Since bases are equal, their powers must also be equal. ...

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Standard VIII

Mathematics

Exponents with like Bases

Solve for x i...

Question

Solve for $x$ in the equation $2^{x + 1} = 8^{x} .$

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\frac{- 1}{3}

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\frac{1}{2}

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Solution

The correct option is D $\frac{1}{2}$
$Given, 2^{x + 1} = 8^{x}$

$2^{x + 1} = (2^{3})^{x} \Rightarrow 2^{x + 1} = 2^{3 x} (∵ (a^{m})^{n} = a^{m n})$

Since bases are equal, their powers must also be equal.

$⟹ x + 1 = 3 x$
$⟹ 2 x = 1$
$⟹ x = \frac{1}{2}$

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Solve for x in the equation 2x+1=8x.

The correct option is D 12 Given, 2x+1=8x 2x+1=(23)x⇒2x+1=23x (∵(am)n=amn) Since bases are equal, their powers must also be equal. ⟹x+1=3x ⟹2x=1 ⟹x=12

Solve for $x$ in the equation $2^{x + 1} = 8^{x} .$

The correct option is D $\frac{1}{2}$
$Given, 2^{x + 1} = 8^{x}$

$2^{x + 1} = (2^{3})^{x} \Rightarrow 2^{x + 1} = 2^{3 x} (∵ (a^{m})^{n} = a^{m n})$

Since bases are equal, their powers must also be equal.

$⟹ x + 1 = 3 x$
$⟹ 2 x = 1$
$⟹ x = \frac{1}{2}$