100.10 ^{3} = \sqrt[x]100 ^{5}
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![100\cdot10 ^{3} = \sqrt[x]{100 ^{5}}\\
10^2\cdot10 ^{3} = \sqrt[x]{(10^2) ^{5}}\\
10^{2+3} = \sqrt[x]{10^{10}}\\
10^5 = 10^{ \frac{10}{x} }\\
5 = \frac{10}{x} }\\
\\x = \frac{10}{5} }\\
x=2\\
S=\{2\}](https://tex.z-dn.net/?f=100%5Ccdot10+%5E%7B3%7D+%3D+%5Csqrt%5Bx%5D%7B100+%5E%7B5%7D%7D%5C%5C%0A10%5E2%5Ccdot10+%5E%7B3%7D+%3D+%5Csqrt%5Bx%5D%7B%2810%5E2%29+%5E%7B5%7D%7D%5C%5C%0A10%5E%7B2%2B3%7D+%3D+%5Csqrt%5Bx%5D%7B10%5E%7B10%7D%7D%5C%5C%0A10%5E5+%3D+10%5E%7B+%5Cfrac%7B10%7D%7Bx%7D+%7D%5C%5C%0A5+%3D++%5Cfrac%7B10%7D%7Bx%7D+%7D%5C%5C%0A%5C%5Cx+%3D++%5Cfrac%7B10%7D%7B5%7D+%7D%5C%5C%0Ax%3D2%5C%5C%0AS%3D%5C%7B2%5C%7D%0A%0A "100\cdot10 ^{3} = \sqrt[x]{100 ^{5}}\\
10^2\cdot10 ^{3} = \sqrt[x]{(10^2) ^{5}}\\
10^{2+3} = \sqrt[x]{10^{10}}\\
10^5 = 10^{ \frac{10}{x} }\\
5 = \frac{10}{x} }\\
\\x = \frac{10}{5} }\\
x=2\\
S=\{2\}")
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