Logarithms Practice Test 1

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Question : 31 of 40

Marks: +1, -0

If

\log _a(ab) = x

, then the value of

\log _b (ab)

is:

$x/{x-1}$
$x/{x+1}$
$x/{ 1-x}$
$1/x$

Solution:

Here,

\log _a(ab) = x

⇒ \log_a a+\log _a b=x

⇒1+\log_a b=x

⇒\log_b a=1/{x-1}

⇒1+\log_b a=1+1/{x-1}

⇒ \log_b b+\log_ba=x/{x-1}

∴\log_b(ab)=x/{x-1}

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