The value of ( log 3 12/ log 36 3)-( log 3 4/ log 108 3) is equal to

Question

The value of ( log 3 12/ log 36 3)-( log 3 4/ log 108 3) is equal to (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

log 3 12 ⋅ log 3 36- log 3 4 ⋅ log 3 108=2(2 log 3 2+1)( log 3 2+1)-(2 log 3 2)(3+2 log 3 2) Let log 3 2= t ∴ 2(2 t+1)(t+1)-2 t(2 t+3)=2(2 t2+3 t+1-2 t2-3 t)=2 × 1=2.

Q. The value of $\frac{l o g _{3} 12}{l o g _{36} 3} - \frac{l o g _{3} 4}{l o g _{108} 3}$ is equal to

1

2

3

4

$lo g_{3} 12 \cdot lo g_{3} 36 - lo g_{3} 4 \cdot lo g_{3} 108 = 2 (2 lo g_{3} 2 + 1) (lo g_{3} 2 + 1) - (2 lo g_{3} 2) (3 + 2 lo g_{3} 2)$
Let $lo g_{3} 2 = t$
$∴ 2 (2 t + 1) (t + 1) - 2 t (2 t + 3) = 2 (2 t^{2} + 3 t + 1 - 2 t^{2} - 3 t) = 2 \times 1 = 2$ .

Q. The value of log36​3log3​12​−log108​3log3​4​ is equal to

1

2

3

4

log3​12⋅log3​36−log3​4⋅log3​108=2(2log3​2+1)(log3​2+1)−(2log3​2)(3+2log3​2) Let log3​2=t ∴2(2t+1)(t+1)−2t(2t+3)=2(2t2+3t+1−2t2−3t)=2×1=2.

Q. The value of $\frac{l o g _{3} 12}{l o g _{36} 3} - \frac{l o g _{3} 4}{l o g _{108} 3}$ is equal to

$lo g_{3} 12 \cdot lo g_{3} 36 - lo g_{3} 4 \cdot lo g_{3} 108 = 2 (2 lo g_{3} 2 + 1) (lo g_{3} 2 + 1) - (2 lo g_{3} 2) (3 + 2 lo g_{3} 2)$
Let $lo g_{3} 2 = t$
$∴ 2 (2 t + 1) (t + 1) - 2 t (2 t + 3) = 2 (2 t^{2} + 3 t + 1 - 2 t^{2} - 3 t) = 2 \times 1 = 2$ .