Question

Solve for n.

Answer 1

\[25^{n-3}=5^{n+8}\]

Answer 2

Which property are we going to use first? :/

Answer 3

Have you considered logarithms, Base 5?

Answer 4

Yes!
So 5^2 is 25
so I replace 5^2 right?

Answer 5

You can start by rewriting 25 as a power of 5.

Answer 6

Correct.

Answer 7

\[5^{2n-3}\]

Answer 8

Right?

Answer 9

so you need common base;

5^5(n-3) = 5^(n+8)

now solve for n
5n-3 = n-8
5n = -5
n= -1

Answer 10

Distributive property.

Answer 11

?? 2n-6

Answer 12

5^5(n-3) = 5^(n+8). Thats the question? <<<

Answer 13

\(25^{n-3}=5^{n+8}\)

\((5^2)^{n-3}=5^{n+8}\)

\(5^{2 (n-3)}=5^{n+8}\)

\(5^{2n-6}=5^{n+8}\)

Answer 14

Now do this:

If \(a^m = a^n\) then m = n.