CATModern Math > Medium393939353535373737333333✅ Correct Option: 1Related questions:CAT 2017 Slot 2If log(2a×3b×5c)\log (2^a \times 3^b \times 5^c)log(2a×3b×5c) is the arithmetic mean of log(22×33×5)\log (2^2 \times 3^3 \times 5)log(22×33×5), log(26×3×57)\log (2^6 \times 3 \times 5^7)log(26×3×57), and log(2×32×54)\log (2 \times 3^2 \times 5^4)log(2×32×54), then a equalsCAT 2017 Slot 1Suppose, log3x=log12y=a\log_3 x = \log_{12} y = alog3x=log12y=a, where x,yx, yx,y are positive numbers. If GGG is the geometric mean of x and y, and log6G\log_6 Glog6G is equal toCAT 2019 Slot 2If xxx is a real number, then loge4x−x23\sqrt{\log_e \frac{4x-x^2}{3}}loge34x−x2 is a real number if and only if