Question #9f0fa

1 Answer
Jul 15, 2017

53.787

Explanation:

Not 100% sure on this one as I get a strange answer...

Changing the constant to a log allows you to start this question:

#2 = log_10(100)#

If it helps, think of the constant as "when I raise 10 to the power of this number, what do I get?". That is the log.

#2 logx# becomes #logx^2#

Similarly, #2log(x+2)# becomes #log(x+2)^2#

Another rule of logs is that if you add them, you multiply the brackets so the equation now becomes:

#log(2x(x^2))=log(100(x+2)^2)#

Now remove the logs as you have one on both sides:

#2x^3=100x^2+400x+400#

#2x^3-100x^2-400x-400=0#

#x^3-50x^2-200x-200=0#

I put this graph into Desmos online as it only has one root and it's a weird decimal. Usually you get something a bit nicer than this so I may have gone a bit wrong somewhere!!