Question

How do you solve `11^ { x - 1} = 1331`?

Answer 1

`x=4`.

Explanation:

`11^(x-1)=1331`.

`:. 11^x*11^-1=1331`.

`:. 11^x=1331*11=11^3*11^1=11^4`.

`:. x=4`.

This root also satisfy the given equation.

`:. x=4` is the solution.

Answer 2

`color(magenta)(x=4`

Explanation:

`11^(x−1)=1331`

`=> 11^(x−1)=11^3`

Since the bases are same on either sides, we equate the powers.

`=> (x−1)=3`

`=>color(magenta)(x=4`

Answer 3

`11^(x-1)=1331`

`rArrx=4`

Explanation:

We can use the properties of logarithms to solve for `x`.

`11^(x-1)=1331`

`rArrln(11^(x-1))=ln1331`

`rArr(x-1)ln11=ln1331`

`rArrx-1=ln1331/ln11`

`rArrx=ln1331/ln11+1`

This is a legitimate solution, but it can be greatly simplified by recognizing that `1331 = 11^3`

Then we can rewrite the equation as:

`rArrx=ln(11^3)/ln11+1`

`rArrx=(3ln11)/ln11+1`

`rArrx=3+1`

`rArrx=4`

It now seems obvious that if we plug `x=4` back into the original expression...

`11^(x-1)=11^(4-1)=11^3=1331`