The ratio (2 log 21 / 4 a -3 log 27( a 2+1)3-2 a /74 log 49 a - a -1) simplifies to

Question

The ratio (2 log 21 / 4 a -3 log 27( a 2+1)3-2 a /74 log 49 a - a -1) simplifies to (A) a2-a-1 (B) a2+a-1 (C) a2-a+1 (D) a2+a+1

Tardigrade Admin · Accepted Answer

(2 log 21 / 4 a -3 log 27( a 2+1)3-2 a /74 log 49 a - a -1)=(24 log 2 a -33 log 33( a 2+1)/74 log 72 a - a -1)=( a 4- a 2-2 a -1/ a 2- a -1)[ a 4-( a -1)2] ⇒ D

Q. The ratio $\frac{2 ^{l o g_{2^{1/4}} a} - 3 ^{l o g_{27} (a^{2} + 1)^{3}} - 2 a}{7 ^{4 l o g_{49} a} - a - 1}$ simplifies to

$a^{2} - a - 1$

$a^{2} + a - 1$

$a^{2} - a + 1$

$a^{2} + a + 1$

$\frac{2 ^{l o g_{2^{1/4}} a} - 3 ^{l o g_{27} (a^{2} + 1)^{3}} - 2 a}{7 ^{4 l o g_{49} a} - a - 1} = \frac{2 ^{4 l o g_{2} a} - 3 ^{3 l o g_{3^{3}} (a^{2} + 1)}}{7 ^{4 l o g_{7^{2}} a} - a - 1} = \frac{a ^{4} - a ^{2} - 2 a - 1}{a ^{2} - a - 1} [a^{4} - (a - 1)^{2}] \Rightarrow D$

Q. The ratio 74log49​a−a−12log21/4​a−3log27​(a2+1)3−2a​ simplifies to

a2−a−1

a2+a−1

a2−a+1

a2+a+1