From the condition, you see that half-life period is given of 5700 years.


As soon as you see it, you write the exponential decay function with the base 
in the form

    m(t) = .    (1)


Here m(t) is the current mass of the radioactive Carbon-14;  is its initial mass;
t is the time after this organism died.


Notice that the degree at    is the ratio of the current time to the given half-time.


           +------------------------------------------------+
           |   So, it is good start and it is RIGHT start.  |
           +------------------------------------------------+


Next, you are given the ratio  ;  so, you divide equation (1) by ,
and you get

     = .


The ratio    is given in the problem: it is 0.15;  so, your equation takes the form

    0.15 = .    (2)


You should solve this exponential equation and find "t" from it.


To solve it, take logarithm base 10 of both sides.  Using standard properties of logarithms, you get

    log(0.15) = .


It gives you

    t =  = 15600.7  years.


In carbon dating problem, it is commonly accepted to round the final computed age to closest hundreds of years.


So, your answer is  15600 years.

     To present a solution in a way how @Theo makes in his post, is WRONG way teaching,
     because under given conditions, when half-life is given, there is no need to use ekt-form of exponential function, AT ALL.

     THEREFORE, to teach as @Theo does in his post, is the same as to teach playing chess game by making obviously wrong first move.


     To solve as @josgarithmetic does in his post, is obviously wrong way to teach beginning students.

     It is so obvious that does not require any explanations.
     Thanks to god, nobody in healthy mind teaches this way.