Question Number 63833 by gunawan last updated on 10/Jul/19
![If the binomial coefficients of 2nd, 3rd and 4th terms in the expansion of [(√2^(log_(10) (10−3^x )) ) + (2^((x−2) log_(10) 3) )^(1/5) ]^m are in AP and the 6th term is 21, then the value(s) of x is(are)](Q63833.png)
$$\mathrm{If}\:\mathrm{the}\:\mathrm{binomial}\:\mathrm{coefficients}\:\mathrm{of}\:\mathrm{2nd},\:\mathrm{3rd} \\ $$$$\mathrm{and}\:\mathrm{4th}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left[\sqrt{\mathrm{2}^{\mathrm{log}_{\mathrm{10}} \left(\mathrm{10}−\mathrm{3}^{{x}} \right)} }\:+\:\sqrt[{\mathrm{5}}]{\mathrm{2}^{\left({x}−\mathrm{2}\right)\:\mathrm{log}_{\mathrm{10}} \mathrm{3}} }\right]^{{m}} \:\mathrm{are}\:\mathrm{in} \\ $$$$\mathrm{AP}\:\mathrm{and}\:\mathrm{the}\:\mathrm{6th}\:\mathrm{term}\:\mathrm{is}\:\mathrm{21},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\left(\mathrm{s}\right) \\ $$$$\mathrm{of}\:{x}\:\:\mathrm{is}\left(\mathrm{are}\right) \\ $$