Question

can someone please solve with explanation​

Answer 1

Answer:

1》x = 7

2》1/ab

3》 28

Step-by-step explanation:

1》

${ \sqrt{3} }^{(x - 3)} = { \sqrt[4]{3} }^{(x + 1)}$

Equalizing the bases —

${3}^{( \frac{x - 3}{2}) } = {3}^{ (\frac{x + 1}{4} )}$

Since bases are equal, exponents must be equal too —

$\frac{x - 3}{2} = \frac{x + 1}{4}$

Cross multiplying —

$4x - 12 = 2x + 2$

Simplifying —

$2x = 14 \: \: \: = > \: \: x = 7 \: \: (ans)$

2》

${(a + b)}^{ - 1} \times ( {a}^{ - 1} + {b}^{ - 1} )$

Converting into fractions —

$\frac{1}{(a + b)} \times ( \frac{1}{a} + \frac{1}{b} )$

Simplifying —

$\frac{1}{(a + b)} \times \frac{(a + b)}{ab} \: \: \: = \: \frac{1}{ab} \: \: (ans)$

3》

$\frac{3 \times {27}^{(n + 1)} \: \: + \: \: 9 \times {3}^{(3n - 1)} }{8 \times {3}^{3n} \: \: - \: \: 5 \times {27}^{n} }$

Equalizing the bases —

$\frac{3 \times {3}^{(3n + 3)} \: \: + \: \: {3}^{2} \times {3}^{(3n - 1)} }{8 \times {3}^{3n} \: \: - \: \: 5 \times {3}^{3n} }$

Simplifying —

$\frac{ {3}^{(3n + 4)} + {3}^{(3n + 1)} }{ {3}^{3n} (8 - 5)}$

Taking common terms —

$\frac{ {3}^{(3n + 1)}( {3}^{3} + 1) }{ {3}^{(3n + 1)} }$

Cancelling —

$( {3}^{3} + 1) = (27 + 1) = 28 \: \: (ans)$

Hope this helps you :)