If log330=1a and log530=1b, then the value of log302 is

log330=1a⇒log303=aSimilarly log305=blog302=log303015=log3030−log3015=1−[log303+log305]=1−a−b

If log330=1a and log530=1b, then the value of log302 is

log330=1a⇒log303=aSimilarly log305=blog302=log303015=log3030−log3015=1−[log303+log305]=1−a−b

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If $\log_{3} 30 = \frac{1}{a}$ and $\log_{5} 30 = \frac{1}{b}$ , then the value of $\log_{30} 2$ is

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$1 - a + b$

$1 + a + b$

$1 - a - b$

$1 + a - b$

answer is A.

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Detailed Solution

$\log_{3} 30 = \frac{1}{a} \Rightarrow \log_{30} 3 = a$

Similarly $\log_{30} 5 = b$

$\log_{30} 2 = \log_{30} \frac{30}{15} = \log_{30} 30 - \log_{30} 15$

$= 1 - [\log_{30} 3 + \log_{30} 5]$

$= 1 - a - b$

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