4^x=7^x-2 zhskdhdvdjd in dve

4^x = 7^(x-2) is the proper way to express this.  Please drop the "zhskdhdvdjd in dve," as it is totally irrelevant here.

Express 4 as e^(ln 4) and 7 as e^(ln 7).  Then

4^x = 7^(x-2) becomes  x*e^(ln 4) = (x-2)*e^(ln 7) = x*e^(ln 7) - 2*e^(ln 7)
                               
 Solving for x:      x [ e^(ln 4) -e^(ln 7) ] = -2*e^(ln 7)
                                          -2(7)           -14
                            x = ---------------- = ----------- = 14/3 (answer)
                                     (4) - (7)              -3