Question

solve this one 15th​

Answer 1

Answer:

(4) 19/48

Step-by-step explanation:

$\sqrt{5\sqrt[3]{5\sqrt{5\sqrt[3]{5\sqrt{5}}}}} = 25^x = 5^{2x}\\\\\Rightarrow5\sqrt[3]{5\sqrt{5\sqrt[3]{5\sqrt{5}}}} = 5^{4x}\\\\\Rightarrow\sqrt[3]{5\sqrt{5\sqrt[3]{5\sqrt{5}}}} = 5^{4x-1}\\\\\Rightarrow5\sqrt{5\sqrt[3]{5\sqrt{5}}}=5^{3(4x-1)}=5^{12x-3}\\\\\Rightarrow\sqrt{5\sqrt[3]{5\sqrt{5}}}=5^{12x-4}\\\\\Rightarrow5\sqrt[3]{5\sqrt{5}}=5^{2(12x-4)}=5^{24x-8}\\\\\Rightarrow\sqrt[3]{5\sqrt{5}}=5^{24x-9}\\\\\Rightarrow5\sqrt{5}=5^{3(24x-9)}=5^{72x-27}\\\\\Rightarrow\sqrt{5}=5^{72x-28}$

$\Rightarrow5=5^{2(72x-28)}=5^{144x-56}\\\\\Rightarrow144x-56=1\\\\\Rightarrow x = \frac{57}{144}=\frac{19}{48}$