2006-09-29 13:20:28 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
64^(-2x+7)=2^(-12x+42)
16^(5x-7)=2^(20x-28)
64^(-2x+7)*16^(5x-7)
=2^(-12x+42+20x-28)
=2^(8x+14)
=4^(4x+7)
log base 4 (4^(4x+7))=4x+7
2006-09-29 14:00:20 · answer #1 · answered by raj 7 · 0⤊ 0⤋
4^(2x) =sixty 4^(x-2) ; sixty 4 = 4^3 so sixty 4^(x-2) = 4^(3x-6) 2 numbers with similar base are equivalent if exponents are equivalent 2x = 3x-6 answer x=6 examine it somewhat works log2 x +log2 (x+3 ) = log2 18 log a +log b = log ab so x(x+3) =18---> x^2+3x-18 =0 answer x=3 log2 (a million/8) = log2 (a million/2^3)= log2 (2^(-3)) answer -3
2016-11-25 03:10:56 · answer #2 · answered by ? 4 · 0⤊ 0⤋
log(4)(64^(-2x + 7) * 16^(5x - 7))
log(4)((4^3)^(-2x + 7) * (4^2)^(5x - 7))
log(4)(4^(3(-2x + 7)) * 4^(2(5x - 7)))
log(4)(4^(-6x + 21) * 4^(10x - 14))
log(4)(4^((-6x + 21) + (10x - 14)))
log(4)(4^(-6x + 21 + 10x - 14))
log(4)(4^(4x + 7))
(4x + 7) * log(4)(4)
(4x + 7) * (log(4)/log(4))
(4x + 7) * 1
ANS : 4x + 7
2006-09-29 14:00:39 · answer #3 · answered by Sherman81 6 · 0⤊ 0⤋
=log_4(64^(-2x+7))+ log_4(16^(5x-7))
=log_4(4^(3(-2x+7)))+ log_4(4^(2(5x-7)))
=3(-2x+7)+2(5x-7)
=-6x+21+10x-14
=4x+7
2006-09-29 13:31:14 · answer #4 · answered by need help! 3 · 0⤊ 0⤋