Please solve the 38th problem Please do not provide any link Please solve as soon as you can - Maths - Indices and Logarithms

Question

Please solve the 38th problem
Please do not provide any link
Please solve as soon as you can as our exams are starting soon
Q 38 Find the value of a, (a ∈ integer) if :
2 a - 5 × 6 2 a - 4 = 1 12 4 × 2

Abhishek Kr. Jha · Accepted Answer

Dear student,
Here is the solution of your asked query:
2a-5×62a-4=1124×2⇒2a-5×2×32a-4=12×2×34×2⇒2a-5×22a-4×32a-4=124×24×34×21⇒2a-5+2a-4×32a-4=124+4+1×34             {using the rule am×an=am+n}⇒23a-9×32a-4=129×34⇒23a-9×29×32a-4×34=1⇒23a-9+9×32a-4+4=1⇒23a×32a=1⇒8a×9a=1⇒8×9a=1⇒72a=1⇒72a=720        {Since any number to the power 0 is 1}comparing powers of both sides as bases are same i
e 72, so we have;a=0
Regards

Please solve the 38th problem. Please do not provide any link. Please solve as soon as you can as our exams are starting soon. Q.38. Find the value of a, (a ∈ integer) if : 2 a - 5 × 6 2 a - 4 = 1 12 4 × 2 .

Please solve the 38th problem.
Please do not provide any link.
Please solve as soon as you can as our exams are starting soon.
Q.38. Find the value of a, (a $\in$ integer) if :
$2^{a - 5} \times 6^{2 a - 4} = \frac{1}{12^{4} \times 2}$ .