Question

Solve the given equation. 5^(1/4)/125^(x/3) =1

Answer 1

x = 0.25

Explanation:

Rewrite the equation as:

`\frac{\sqrt[4]{5}}{125^(x/3)} = 1`

`\sqrt[4]{5} = 125^(x/3)`

`(\sqrt[4]{5})^4 = (125^(x/3))^4`

`5 = 125^(4x/3)`

`ln5 = ln(125^(4x/3))`

`ln5 = (4x)/(3)ln125`

`x = (3)/(4)(ln5)/(ln125) = (3)/(4)(1)/(3) = (1)/(4) = 0.25`