The number of roots of the equation xlog3x-x-1 is-are

The correct option is A 2 Substitute log_3x=t The equation becomes 3^t^2× 3^t/2 =1 ⇒ 3^t^2+t/2=1 ⇒ t^2+t2=0 t=0 or t= 12 Ea ...

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Standard XII

Mathematics

nth Root of a Complex Number

The number of...

Question

The number of roots of the equation $x^{{log}_{3} x} \sqrt{x} = 1$ is/are

1

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2

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3

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0

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Solution

The correct option is A $2$
Substitute ${log}_{3} x = t$
The equation becomes
$3^{t^{2}} \times 3^{\frac{t}{2}} = 1$
$\Rightarrow 3^{t^{2} + \frac{t}{2}} = 1$
$\Rightarrow t^{2} + \frac{t}{2} = 0$
$t = 0$ or $t = - \frac{1}{2}$
Each value of $t$ will give one value of $x$ . Hence, there are two solutions.

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The number of roots of the equation xlog3x√x=1 is/are

The correct option is A 2Substitute log3x=tThe equation becomes 3t2×3t2=1⇒3t2+t2=1⇒t2+t2=0t=0 or t=−12Each value of t will give one value of x. Hence, there are two solutions.

The number of roots of the equation $x^{{log}_{3} x} \sqrt{x} = 1$ is/are