How do you solve #6^x=72#?

1 Answer
Dec 2, 2016

Answer:

#x≈2.387#

Explanation:

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

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(logx^n=nlogx)color(white)(2/2)|)))#
#color(white)(xxxxxxx)"Applies to logs in any base."#

Take the natural log ( ln) of both sides.

#rArrln6^x=ln72#

Using the above law.

#xln6=ln72#

#rArrx=ln72/ln6≈2.387" to 3 decimal places"#