Question

then find the value of x ? ​

Answer 1

$\huge\mathfrak{\bf{\underline{\underline{Answer \ :}}}}$

${\dag} \: {\underline{\boxed{\sf{\purple{ Refer \ Attachment \ For \ Property \ Of \ Indices}}}}}$

${( \frac{p}{q}) }^{x - 1} = {( \frac{q}{p}) }^{2x - 3} \\ { (\frac{q}{p} )}^{ \frac{1}{ x - 1} } = {( \frac{q}{p}) }^{2x - 3}$

By Property Of Indices

$\frac{1}{x - 1} = 2x - 3 \\ 1 = (x - 1) \times (2x - 3) \\ 1 = {2x}^{2} - 3x - 2x + 3 \\ 2 {x}^{2} - 5x + 2 = 0 \\ 2 {x}^{2} - 4x - x + 2 = 0 \\ 2x(x - 2) \: \: - 1(x + 2) = 0 \\ now \\ \: \: x - 2 = 0 \: \: or \: 2x - 1 = 0 \\ x = 2 \: \: or \: \: x = \frac{1}{2}$

Answer 2

Answer:

(

q

p

)

x−1

=(

p

q

)

2x−3

(

p

q

)

x−1

1

=(

p

q

)

2x−3

By Property Of Indices

\begin{gathered}\frac{1}{x - 1} = 2x - 3 \\ 1 = (x - 1) \times (2x - 3) \\ 1 = {2x}^{2} - 3x - 2x + 3 \\ 2 {x}^{2} - 5x + 2 = 0 \\ 2 {x}^{2} - 4x - x + 2 = 0 \\ 2x(x - 2) \: \: - 1(x + 2) = 0 \\ now \\ \: \: x - 2 = 0 \: \: or \: 2x - 1 = 0 \\ x = 2 \: \: or \: \: x = \frac{1}{2}\end{gathered}

x−1

1

=2x−3

1=(x−1)×(2x−3)

1=2x

2

−3x−2x+3

2x

2

−5x+2=0

2x

2

−4x−x+2=0

2x(x−2)−1(x+2)=0

now

x−2=0or2x−1=0

x=2orx=

2

1