Question

Solve for n: 4^n×2^-18=1​

Answer 1

n = 9.

Explanation:

4^n = 1 / 2^-18

4^n = 2^18

2^2n = 2^18

2n = 18

n = 9.

Answer 2

One way to do it is by cleverly rewriting terms and using some basic algebraic identities:

`4^n\cdot 2^(-18)=1`.

`2^(2n-18)=2^0`.

`2n-18=0`.

`n=18/2=\boxed{9}`.

Another way would be to use logarithms, namely:

`4^n\cdot2^(-18)=1\implies n=\log_4\Big({(1)/(2^(-18))}\Big)=\boxed{9}`.

Hope this helps.