andreygoncharovmath andreygoncharovmath
  • 02-04-2022
  • Mathematics
contestada

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

Respuesta :

loneguy
loneguy loneguy
  • 02-04-2022

[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]

Answer Link

Otras preguntas

What are three ways that rivers and streams change Earth's surface?
Which were part of ancient Egyptian civilization? Choose all answers that are correct. A. longest continuous civilization in the world B. civilization c
If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same, what is the formula to find
Draw a line with the given slope through the given point. (3, -2) slope =-3
What are 10 facts about tornadoes?Science
a curved, transparent object used to refract light
What is GOOD in Spanish?
Being prepared to play is an important step in staying safe when participating in a game. True false
six ways that the human rights violation unfluences individual,groups and broader south african community
The cell that does not have a cell wall is the