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

2 Answers
Sep 19, 2016

Answer:

≈ 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

Answer:

#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#