Answer:
x = 0.25
Step-by-step explanation:
Rewrite the equation as:
[tex]\frac{\sqrt[4]{5}}{125^{x/3}} = 1[/tex]
[tex]\sqrt[4]{5} = 125^{x/3}[/tex]
[tex](\sqrt[4]{5})^4 = (125^{x/3})^4[/tex]
[tex]5 = 125^{4x/3}[/tex]
[tex]ln5 = ln(125^{4x/3})[/tex]
[tex]ln5 = \frac{4x}{3}ln125[/tex]
[tex]x = \frac{3}{4}\frac{ln5}{ln125} = \frac{3}{4}\frac{1}{3} = \frac{1}{4} = 0.25[/tex]
