Question

find the value of x for this equation​

Answer 1

root 5 *root 5*root 5 * root 5=125^x/4

root 5 * root 5 *root 5 *5^1/2 =5^3x/4

root 5 * root 5 *root 5^3/2 = 5^3x/4

root 5 * root 5 * 5^3/4 = 5^3x/4

root 5 * root 5^7/4 =5^3x/4

root 5 *5^7/8 = 5^3x/4

root 5^15/8 = 5^3x/4

5^15/16=5^3x/4

15/16 = 3x/4

20=16x

x=5/4

Answer 2

$\sqrt{5\sqrt{5\sqrt{5\sqrt{5} } } } = 125^{x/4}\\ \\\sqrt{5\sqrt{5\sqrt{5*5^{1/2} } } }=125^{x/4}\\\\\sqrt{5\sqrt{5\sqrt{5^{3/2} } } }=125^{x/4}\\\\\sqrt{5\sqrt{5*(5^{3/2})^{1/2} } }=125^{x/4}\\\\\sqrt{5\sqrt{5*(5^{3/4}) } }=125^{x/4}\\\\\sqrt{5\sqrt{5^{7/4} } }=125^{x/4}\\\\\sqrt{5*(5^{7/4})^{1/2} }=125^{x/4}\\\\\sqrt{5*(5^{7/8}) }=125^{x/4}\\\\\sqrt{5^{15/8} }=125^{x/4}\\\\(5^{15/8})^{1/2}=125^{x/4}\\\\(5^{15/16})=125^{x/4}\\\\5^{(15/16)}=5^{3x/4}$

$\frac{15}{16}=\frac{3x}{4}\\ \\\frac{5}{4}=\frac{x}{1} \\ \\4x=5$

$x=\frac{5}{4}$

Hence, option (iv) is correct.