Solve for x 2-3x- 8-3x - 1-2-2-1-2-1-2-

The correct option is C 1/2 Given 2^3x = 8^3x + 1 ⇒ 2^3x = ( 2^3)^3x + 1 ⇒ 2^3x = 2^9x + 3 (∵ (a^m)^n = (a)^m × n) Since the bases are equal, the exp ...

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Byju's Answer

Standard IX

Mathematics

Normal Form to Standard Form

Solve for x 2...

Question

Solve for $x$

$2^{3 x} = 8^{3 x + 1}$

$\frac{- 1}{2}$

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$\frac{1}{2}$

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-2

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Solution

The correct option is A
$\frac{- 1}{2}$

Given

$2^{3 x} = 8^{3 x + 1}$

$\Rightarrow 2^{3 x} = (2^{3})^{3 x + 1}$

$\Rightarrow 2^{3 x} = 2^{9 x + 3}$ ( $∵ (a^{m})^{n} = (a)^{m \times n}$ )

Since the bases are equal, the exponents should also be equal

$\Rightarrow 3 x = 9 x + 3$

$\Rightarrow - 6 x = 3$

$\Rightarrow x = \frac{- 1}{2}$

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Solve for x 23x = 83x+1

The correct option is A −12 Given 23x = 83x+1 ⇒ 23x = (23)3x+1 ⇒ 23x = 29x+3 (∵(am)n = (a)m×n) Since the bases are equal, the exponents should also be equal ⇒3x=9x+3 ⇒−6x=3 ⇒ x= −12

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