Question

If (64)to the power 2a-5 equals to 4*8to th power ,find the value?!!!!!! please answer this ​

Answer 1

Answer:

64^(2a-5) = 2² * (2³)^(a-5)

=> (2^6)^(2a-5) = 2²*2^(3a-15)

=> 2^(12a-30) = 2^(2+3a-15)

=> 2^(12a-60) = 2^(3a-13)

=> 12a - 30 = 3a-13

=> 9a = 17

=> a = 17/9

Answer 2

Find the value of a

$64^{(2a-5)} = 4 * 8^{(a-5)} \\\\2^{(6)(2a-5)} = 2^{2} * 2^{(3)(a-5)} \\ \\ 2^{(12a-30)} = 2^{(2+3a-15)} \\\\Since, the \: bases \: are \: equal,\\Therefore, the\: powers \: will \: be \: equated.\\\\12a - 30 = 3a - 13\\\\12a - 3a = -13 + 30\\\\9a = 17\\\\a = 17/9$

Properties Used above :-

$(1) \: a^{m}*a^{n} = a^{(m+n)}\\\\ (2) \: a^{x} = a^{y} \\\\then,\\\\x = y$