The correct options are A log_10a/log_10b B log_ea/log_eb Log_ba=log_ma/log_mb [Properties of logarithm where m 0] So ...

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Fundamental Laws of Logarithms

log b a=?

Question

$l o g_{b} a = ?$

\frac{l o g_{10} a}{l o g_{10} b}

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$\frac{l o g_{e} a}{l o g_{e} b}$

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\frac{l o g_{10} b}{l o g_{10} a}

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$\frac{l o g_{e} a}{l o g_{e} b}$

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Solution

The correct options are
A $\frac{l o g_{10} a}{l o g_{10} b}$
B
$\frac{l o g_{e} a}{l o g_{e} b}$

$L o g_{b} a = \frac{l o g_{m} a}{l o g_{m} b}$ [Properties of logarithm where $m > 0$ ]

So, $L o g_{b} a = \frac{l o g_{1} 0 a}{l o g_{1} 0 b}$ (Option A is correct)

$L o g_{b} a = \frac{l o g_{e} a}{l o g_{e} b}$ (Option B is also correct)

Option C $&$ option D are

$L o g_{a} b = \frac{l o g_{10} b}{l o g_{10} a} = \frac{l o g_{e} b}{l o g_{e} a}$

Only option A and B are correct.

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