If _4 5 = a and _5 6 = b, then _3 2 is equal to - Vidyadip

MCQ

If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to

A
${1 \over {2a + 1}}$
B
${1 \over {2b + 1}}$
C
$2ab + 1$
✓
${1 \over {2ab - 1}}$

✓

Answer

Correct option: D.

${1 \over {2ab - 1}}$

d
(d) $ab = {\log _4}5.{\log _5}6 = {\log _4}6 = {1 \over 2}{\log _2}6$

$ab = {1 \over 2}(1 + {\log _2}3) \Rightarrow 2ab - 1 = {\log _2}3$

$\therefore {\log _3}2 = {1 \over {2ab - 1}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from basic of algoritham→basic of algoritham — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The set $A = \{ x:x \in R,\,{x^2} = 16$ and $2x = 6\} $ equals

If a parallelopiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is:

If $^n{C_{r - 2}} = 36$ , $^n{C_{r - 1}} = 84$ and $^n{C_r} = 126$ , then value of $^n{C_{2r}}$ is

If sum of distances of a point from the origin and lines $x = 2$ is $4$, then its locus is

The third term of a $G.P.$ is the square of first term. If the second term is $8$, then the ${6^{th}}$ term is

A = (1, 1, 4) and B = (5, -3, 4) are two points. If the points P, Q are on the line AB such that AP = PQ = QB then PQ =

n(n + 1) (n + 5) is a multiple of ____ for all n ∈ N

One card is drawn from a pack of $52$ cards.The probability of getting a $10$ of black suit is:

If the roots of the equation $q{x^2} + px + q = 0$ where $p, q$ are real, be complex, then the roots of the equation ${x^2} - 4qx + {p^2} = 0$ are

In an increasing geometric progression ol positive terms, the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the third and fifth terms is $49$. Then the sum of the $4^{\text {th }}, 6^{\text {th }}$ and $8^{\text {th }}$ terms is :-