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[tex]\sqrt{7^{16}} = 7^n\\\\\implies \left(7^{16}\right)^{\tfrac 12} = 7^n\\\\\implies 7^{\left(\tfrac 12 \times 16\right)}=7^n\\\\\implies 7^8 = 7^n\\\\\implies \ln 7^8 = \ln 7^n\\\\\implies 8\ln 7 = n \ln 7\\\\\implies n =8[/tex]