Question

Pls somebody answer this ques i am in desperate need!

Answer 1

Answer:

Solution:-

$\sf \implies\sf \: \frac{3 {}^{3x} \times 3 {}^{2x} }{3 {}^{x} } = \sqrt[4]{3 {}^{20} } \\ \\ \sf \implies \frac{3 {}^{5x} }{5x} = \bigg(3 {}^{ \cancel{20}} {}^{ {}^{5} } \bigg) {}^{ \cancel{ \frac{1}{4}} } \\ \\ \sf \implies \cancel3 {}^{4x} = \cancel3 {}^{5} \\ \\ \sf \implies \: 4x = 5 \\ \\ \sf \implies\bold{ \red{x = \frac{5}{4}}}$

Hence This is Answer.

Answer 2

$\sf\huge\bold{Answer:}$

Given :

$\tt\ \frac{3 {}^{3x } \times {3}^{2x} }{ {3}^{x} } = \sqrt[4]{ {3}^{20} }$

To find :

Value of x

Solution :

$\tt{ \frac{3 {}^{3x } \times {3}^{2x} }{ {3}^{x} } = \sqrt[4]{ {3}^{20} } }$

Formulas used :

$\boxed{ \bf \red{{a}^{m} \times {a}^{n} = {a}^{m + n}} }$

$\tt\boxed{ \bf \red{ {a}^{m} \div {a}^{n} = \frac{a {}^{m} }{a {}^{n} } = {a}^{m - n} } }$

$\boxed{\bf \red{ \: \sqrt[x]{y} = (y) {}^{ \frac{1}{x} } } }$

$\boxed{\bf \red{(a {}^{m}) {}^{n} = a {}^{m \times n} }}$

$:⟶ \: \tt\ \frac{ {3}^{3x + 2x} }{ {3}^{x} } = ( {3}^{20} ) {}^{\frac{1}{4} }$

$\tt\ :⟶ \frac{3 {}^{5x} }{3 {}^{x} } = 3 {}^{ \frac{20}{4} }$

$\tt\ :⟶ 3 {}^{5x - x} = 3 {}^{ \cancel \frac{20}{4} } {}^{ \frac{5}{1} }$

$\tt\ :⟶ {3}^{4x} = {3}^{5}$

Since, base are Same, powers can be compared separately.

$\implies \tt \: 4x = 5$

$\implies \tt \: x = \frac{5}{4}$

Hence,

$\huge\boxed{ \tt \purple{x = \frac{5}{4} }}$