If l o g 4 5 = a and l o g 5 6 = b, then l o g 3 2 is equal to Options: A . &nbsp 1 2 a + 1 B . &nbsp 1 2 b + 1 C . &nbsp 2 a b + 1 D . &nbsp 1 2 a b − 1

Answer: Option D : D a b = l o g 4 5. l o g 5 6 = l o g 4 6 = 1 2 l o g 2 6 a b = 1 2 ( 1 + l o g 2 3 ) ⇒ 2 a b − 1 = l o g 2 3 ∴ l o g 3 2 = 1 2 a b − 1

If log4 5 = a and log5 6 = b, then log3 2 is equal to

Question

If $l o g_{4}$ 5 = a and $l o g_{5}$ 6 = b, then $l o g_{3}$ 2 is equal to

Options:

A .

\frac{1}{2 a + 1}

B .

\frac{1}{2 b + 1}

C .

2 a b + 1

D .

\frac{1}{2 a b - 1}

Answer: Option D
:
D

a b = l o g_{4} 5. l o g_{5} 6 = l o g_{4} 6 = \frac{1}{2} l o g_{2} 6

a b = \frac{1}{2} (1 + l o g_{2} 3) \Rightarrow 2 a b - 1 = l o g_{2} 3

∴ l o g_{3} 2 = \frac{1}{2 a b - 1}

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