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

##### 2 Answers

Sep 19, 2016

≈ 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"#

Sep 19, 2016

#### Explanation:

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