Question

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Answer 1

Answer:

2^(a-5) . (2×3)^(2a-4)= 2^{(a-5)+(2a-4)} .3^(2a-4)

and 1/(12^4)(2) = 3^(-4)×2^(-9).

so let's equate powers of same bases i.e.,

power of 3:- 2a-4= -4 ; a=0

power of 2:- 3a-9= -9 ; a=0

so finally the value of a is zero.

thank you

Answer 2

Question:-

${2}^{a - 5} \times {6}^{2a - 4} = \frac{1}{ {12}^{4} \times 2}$

Solution:-

$= {2}^{a - 5} \times {6}^{2a - 4} = \frac{1}{ {12}^{4} \times 2} \\ = {2}^{a - 5} \times {6}^{2a - 4} = \frac{1}{ {3}^{4} \times { ({2}^{2} )}^{4} \times {2}^{1} } \\ = {2}^{a - 5} \times {6}^{2a - 4} = \frac{1}{ {3}^{4} \times {2}^{8} \times {2}^{1} } \\ = {2}^{a - 5} \times {6}^{2a - 4} = \frac{1}{ {3}^{4} \times {2}^{4} \times {2}^{5} } \\ = {2}^{a - 5} \times {6}^{2a - 4} = \frac{1}{ {(2 \times 3)}^{4} \times {2}^{5} } \\ = {2}^{a - 5} \times {6}^{2a - 4} = {(6)}^{ - 4} \times {(2)}^{ - 5}$

Therefore, by comparing,

→a - 5 = (-5)

=> a =( -5) + 5

=> a = 0

(and)

→2a - 4 = (-4)

=> 2a = (-4) + 4

=> a = 0

__________________________

Therefore,

$\huge\rm{\boxed{ a = 0 }}$

Concept used:-

Concept :- Exponential concepts

Marks :- 4 (or) 5 marks

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