Answer:
[tex]( \frac{a}{b} ) {}^{x - 1} = ( \frac{b}{a} ) {}^{x - 3} \\ \\ ( \frac{a}{b} ) {}^{x - 1} = ( \frac{a}{b} ) {}^{ - (x - 3)}[/tex]
Here, bases of both the sides are same.
[tex]x - 1 = - (x - 3) \\ x - 1 = - x + 3 \\ x + x = 3 + 1 \\ 2x = 4 \\ \\ x = \frac{4}{2} \\ \\ x = 2[/tex]
Hence, value of x = 2.
In these type of exponential problems you firstly need to make the bases equal then you can equate the powers to get the value of x
1) Here b/a is the reciprocal of a/b so for making bases equal you can write b/a as a/b^-1
2) After that you can just equate the powers directly and get the power of x.
Attaching a solved explanation too
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Answer:
[tex]( \frac{a}{b} ) {}^{x - 1} = ( \frac{b}{a} ) {}^{x - 3} \\ \\ ( \frac{a}{b} ) {}^{x - 1} = ( \frac{a}{b} ) {}^{ - (x - 3)}[/tex]
Here, bases of both the sides are same.
[tex]x - 1 = - (x - 3) \\ x - 1 = - x + 3 \\ x + x = 3 + 1 \\ 2x = 4 \\ \\ x = \frac{4}{2} \\ \\ x = 2[/tex]
Hence, value of x = 2.
Answer:
In these type of exponential problems you firstly need to make the bases equal then you can equate the powers to get the value of x
1) Here b/a is the reciprocal of a/b so for making bases equal you can write b/a as a/b^-1
2) After that you can just equate the powers directly and get the power of x.
Attaching a solved explanation too