Question

How do you solve `2*20^n=18`?

Answer 1

≈ 0.733

Explanation:

Using the `color(blue)"law of logarithms"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(lnx^n=nlnx)color(white)(a/a)|)))`

The first step here is to divide both sides by 2.

`rArr20^n=9`

To obtain n as a multiplier rather than as an index, take ln of both sides.

`rArrln20^n=ln9`

`rArrnln20=ln9`

`rArrn=(ln9)/(ln20)≈0.733" to 3 decimal places"`

Answer 2

`n = 0.73345`

Explanation:

`2xx20^n= 18" "larr div2`

`20^n = 9`

9 is clearly not a power of 20, so logs are indicated.

`log20^n= log9`

`nlog20 = log9`

`n = log9/log20`

`n = 0.73345`