Question

if
$( {12 \div 13)}^{4 } ( {13 \div 12})^{ - 8} = ( {12 \div 13)}^{2x}$
then find the value of x. ​

Answer 1

Answer:

x=6

Step-by-step explanation:

We can also write the question as,

$(\frac{12}{13} )^{4}$  $(\frac{13}{12})^{-8}=(\frac{12}{13})^{2x}$

=> $(\frac{12}{13})^{4}(\frac{12}{13})^{8}=(\frac{12}{13})^{2x}$  (because $x^{-2} =(\frac{1}{x})^{2}$)

=> $(\frac{12}{13})^{4+8}=(\frac{12}{13})^{2x}$      (because $(x)^{2}(x)^{4}=(x)^{2+4}$)

=> $(\frac{12}{13})^{12}=(\frac{12}{13})^{2x}$

Equating the powers, we get,

12=2x

=> x=6

Hope it helps :)

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