Question

Determinati numarul natural x astfel incat :
a) (2 la puterea 3 * 3 la puterea 5 ) la puterea 2 :(2 la puterea 4 * 3 la puterea 6 ) :3 la puterea 2 = 6 la puterea x
b) (4 * 8 ) la puterea 15 : 4 la puterea 5 : 2 la puterea 6 =2 la puterea x

Answer 1

a) (2⁶x3¹°):(2⁴x3⁶):3²=(2x3)^X
2⁶⁻⁴x3¹°⁻⁶⁻²=(2x3)^X
2²x3²=(2x3)^X
(2x3)²=(2x3)^X
X=2

b) (2²)¹⁵x(2³)¹⁵:(2²)⁵:2⁶=2^X
2³°x2⁴⁵:2¹°:2⁶=2^X
2³°⁺⁴⁵⁻¹°⁻⁶=2^X
2⁵⁹=2^X
X=59