Question

ayuda
...................

Answer 1

Respuesta:

13. A) 6

14. C) 14

15. E) 6

16. C) 3

17. B) 1/2

Explicación paso a paso:

13.

$A^{6y+10} . A^{2-4y} = ((A^{2} )^{3} )^{4} \\A^{6y+10 + 2-4y} = A^{2(3)(4)}\\6y + 10 + 2 - 4y = 2(3)(4)\\2y + 12 = 24\\2y = 24 - 12\\2y = 12\\y = \frac{12}{2} \\y = 6$

14.

$3125^{x-2} =625^{x+1}\\5^{5(x-2)} =5^{4(x+1)} \\5(x-2) = 4(x+1)\\5x - 10 = 4x + 4\\5x - 4x = 4 + 10\\x = 14$

15.

$(16^{x} )^{3} =((8^{2} )^{4} )^{3}\\(2^{4} ^{(x)} )^{3} =((2^{3} ^{(2)} )^{4} )^{3}\\2^{12x} =2^{72} \\12x = 72\\x = \frac{72}{12}\\x = 6$

16.

Reemplaza con "x = 3" y si cumple.

$(2^{2^{x+2} } )^{2^{x-4} } =2^{16}\\(2^{2^{3+2} } )^{2^{3-4} } =2^{16}\\65536=65536$

17.

$81^{3^{2x} } =27^{4^{2x} } \\\ln \left(4\right)+2x\ln \left(3\right)=\ln \left(3\right)+2x\ln \left(4\right)\\x = \frac{1}{2}$