Solve for x in the equation 2-x-1-8-x-1-31-213

The correct option is B 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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Byju's Answer

Standard VIII

Mathematics

Laws of Exponents

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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Similar questions

Solve the following equations for x:

(i) $7^{2 x + 3} = 1$

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

(iii) $2^{5 x + 3} = 8^{x + 3}$

(iv) $4^{2 x} = \frac{1}{32}$

(v) $4^{x - 1} \times (0.5)^{3 - 2 x} = {(\frac{1}{8})}^{x}$

(vi) $2^{3 x - 7} = 256$

Q. Solve the matrix equation

[\begin{matrix} 5 & 4 \\ 1 & 1 \end{matrix}] X = [\begin{matrix} 1 & - 2 \\ 1 & 3 \end{matrix}]

, where X is a 2 × 2 matrix.

Q. Solve for

x

in the equation

2^{x + 1} = 8^{x} .

Q. Solve the following equation for

x

:

v)

4^{x - 1} \times (0.5)^{3 - 2 x} = {(\frac{1}{8})}^{x}

Solve for x

4^x-1* (0.5)^3-2x=(1/8)^x

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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.

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