Question

please help me in this problem​

Answer 1

Heya✌

Q u e s t i o n:

${125}^{ - 2} \div {625}^{ 1 - x} = {5}^{2x}$

S o l u t i o n:

${125}^{ - 2} \div {625}^{ 1 - x} = {5}^{2x} \\( {25}^{2} {)}^{ - 2} \div (2 {5}^{3} {)}^{1 - x} = {5}^{2x} \\ {25}^{ - 4} \div {25}^{3 - 3x} = {5}^{2x} \\ {25}^{ - 4 - (3 - 3x)} = {5}^{2x} \\ {25}^{ - 4 - 3 + 3x} = {5}^{2x} \\ ({5}^{2} {)}^{ - 4 - 3 + 3x} = {5}^{2x} \\ {5}^{ - 8 - 6 + 6x} = {5}^{2x} \\ - 14 + 6x = 2x \\ - 14 = 2x - 6x \\ - 14 = - 4x \\ \\ x = \frac{14}{4} \\ x = \frac{7}{2}$

A n s w e r = 7/2