Question

My directions say to solve the exponential equation.

81^7x = 9

Answer 1

write 81 as 3^4 and 9 as 3^2
then solve it

Answer 2

When you see these types of problems, look to see if you can make both sides have the same "base" 9 in this case.
notice that 9^2 = 81
so you can rewrite this as
\[ (9^2)^{7x} = 9^1 \]

Answer 3

use the rule
\[ (x^y)^z = x^{yz} \]
so you get
\[ 9^{14x} = 9^1 \]

Answer 4

this means 14x = 1
solve for x

Answer 5

Thank you.