Let `a >1`be a real number. Then the number of roots equation `a^(2(log)_2x)=15+4x^((log)_2a)`is2 (b) infinite (c)0 (d) 1

Let `a >1`be a real number. Then the number of roots equation `a^(2(lo

1.	Let `a >1`be a real number. Then the number of roots equation `a^(2(log)_2x)=15+4x^((log)_2a)`is2 (b) infinite (c)0 (d) 1
Answer» `a^(2log_2^x)=15+4x^(log_2^a)` `a>1` `(a^(log_2^x))^2=15+4x^(log_2^a)` `(x^(log_2^a))^2=15+4x^(log_2^a)` `x>0` Let `x^(log_2^a)=t` `log_2^a` is positive `t^2=15+4t` `t^2-4t-15=0` `t=(4pmsqrt(16+60))/2=(4pmsqrt(76))/2` `t=2+sqrt19` `t=2-sqrt19` this is not possible Number of solution=1.