Question

find the value of x if (√3)^x=3^7

Answer 1

Answer:

x = 14

Step-by-step explanation:

Given that ;

$\sf ( \sqrt{3}) {}^{x} = 3 {}^{7} \\ \\ \implies \sf ( \sqrt{3}) {}^{x} = \{( \sqrt{3} ) {}^{2} \} {}^{7} \\ \\ \implies \sf ( \sqrt{3}) {}^{x} = ( \sqrt{3} ) {}^{14}$

Since, bases are same. They can be cancelled.

$\boxed{ \red{\bf \therefore \: x = 14}}$

Hence, the value of x is 14.

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$\large{\underline{\underline{\mathfrak{\heartsuit \: Exponent\: Rules: \: \heartsuit}}}}$

$\sf \odot \: \: (a)^m* (a)^n = a^{mn}\\\\\sf \odot \: \: (a^m) * (b^m) = (ab)^m \\\\\sf \odot \: \: a^0 = 1\\\\\sf \odot \: \: a^{-1}= \frac{1}{a}$

Answer 2

Solution:-

(√3)^x=3^7

=>(√3)^x= {(√3)^2}^7

=>(√3)^x=(√3)^14

=>x=14

${Because\: we\:know\: if (a)^x = (a)^y => x=y}$

•°• The value of "x" is 14