If Log2 = 0.3010 And 3=0.4771, The Value Of Log5 512 Is?

If log2 = 0.3010 and 3=0.4771, the value of log5 512 is?

3.876
3.89
3.987
3.098

Explanation

$l o g_{5} 512 = \frac{l o g 5 1 2}{l o g 5}$
$= \frac{l o g 2 ^{9}}{l o g ( 1 0 / 2 )}$
$= \frac{9 l o g 2}{l o g 1 0 - l o g 2}$
$= \frac{9 \times 0 . 3 0 1 0}{1 - 0 . 3 0 1 0}$
$= \frac{2 . 7 0 9}{0 . 6 9 9}$
$= \frac{2 7 0 9}{6 9 9}$
$= 3.876$

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If log2 = 0.3010 and 3=0.4771, the value of log5 512 is?

Explanation

$l o g_{5} 512 = \frac{l o g 5 1 2}{l o g 5}$
$= \frac{l o g 2 ^{9}}{l o g ( 1 0 / 2 )}$
$= \frac{9 l o g 2}{l o g 1 0 - l o g 2}$
$= \frac{9 \times 0 . 3 0 1 0}{1 - 0 . 3 0 1 0}$
$= \frac{2 . 7 0 9}{0 . 6 9 9}$
$= \frac{2 7 0 9}{6 9 9}$
$= 3.876$

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If log2 = 0.3010 and 3=0.4771, the value of log5 512 is?

Explanation

log5​512=log5log512​=log(10/2)log29​=log10−log29log2​=1−0.30109×0.3010​=0.6992.709​=6992709​=3.876

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$l o g_{5} 512 = \frac{l o g 5 1 2}{l o g 5}$
$= \frac{l o g 2 ^{9}}{l o g ( 1 0 / 2 )}$
$= \frac{9 l o g 2}{l o g 1 0 - l o g 2}$
$= \frac{9 \times 0 . 3 0 1 0}{1 - 0 . 3 0 1 0}$
$= \frac{2 . 7 0 9}{0 . 6 9 9}$
$= \frac{2 7 0 9}{6 9 9}$
$= 3.876$