Question

Question #9f0fa

Answer 1

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!!