Question

The square root of 7^16 is equal to 7^n for some positive integer n. Find n.

Answer 1

`\sqrt{7^(16)} = 7^n\\\\\implies \left(7^(16)\right)^(\tfrac 12) = 7^n\\\\\implies 7^(\left(\tfrac 12 * 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`