Please solve this ::

The number of integers satisfying the inequality $\sqrt{\log_{\frac{1}{2}}^{2} x + 4 \log_{2} \sqrt{x}} < \sqrt{2} (4 - \log_{16} x^{4})$ are
(A) 2
(B) 3
(C) 4
(D) 5

Question

Please solve this ::

The number of integers satisfying the inequality log 1 2 2 x + 4
log 2 x < 2 4 - log 16 x 4 are
(A) 2
(B) 3
(C) 4
(D) 5

Zuhaib Ul Zamann · Accepted Answer

Dear student, log12x=-log2xlog2x=12logxlog16x4=44log2x=log2xPut log2x=tHence the inequality becomest2+2t<24-tSince LHS>0We have 4-t>0t<4Squaring both sides we gett2+2t<216+t2-8tt2-18t+32>0t-92>49As t<4we have t-9<-7t<2Also t2+2t≥0tt+2≥0t∈(-∞,-2]∪[0,∞)Hence t∈(-∞,-2]∪[0,2)x∈(0,14]∪[1,4)Regards

Please solve this :: The number of integers satisfying the inequality log 1 2 2 x + 4 log 2 x < 2 4 - log 16 x 4 are (A) 2 (B) 3 (C) 4 (D) 5

Please solve this ::

The number of integers satisfying the inequality $\sqrt{\log_{\frac{1}{2}}^{2} x + 4 \log_{2} \sqrt{x}} < \sqrt{2} (4 - \log_{16} x^{4})$ are
(A) 2
(B) 3
(C) 4
(D) 5