Solve for x34 x -1-27 x -1A- -2B- 1C- 2D- -1

The correct option is C 2 Given 3^4x + 1 = 27^x + 1 ⇒ 3^4x + 1 = ( 3^3)^x + 1 ⇒ 3^4x + 1 = 3^3x + 3 (∵ (a^m)^n = (a)^m × n) Since the bases are equ ...

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Standard IX

Mathematics

Normal Form to Standard Form

Solve for x34...

Question

Solve for $x$

$3^{4 x + 1} = 27^{x + 1}$

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Solution

The correct option is B
2

Given

$3^{4 x + 1} = 27^{x + 1}$

$\Rightarrow 3^{4 x + 1} = (3^{3})^{x + 1}$

$\Rightarrow 3^{4 x + 1} = 3^{3 x + 3}$ ( $∵ (a^{m})^{n} = (a)^{m \times n}$ )

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

$\Rightarrow 4 x + 1 = 3 x + 3$

$\Rightarrow x = 2$

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Q. Solve for

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3^{4 x + 1} = (27)^{x + 1}

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Solve for x 34x+1 = 27x+1

The correct option is B 2 Given 34x+1 = 27x+1 ⇒ 34x+1 = (33)x+1 ⇒ 34x+1 = 33x+3 (∵(am)n = (a)m×n) Since the bases are equal, the exponents should also be equal ⇒4x+1=3x+3 ⇒ x=2

Solve for $x$

$3^{4 x + 1} = 27^{x + 1}$