How do you evaluate $ln 432 = y$ $Ln 432 = y$ ?

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How do you evaluate $ln 432 = y$ $Ln 432 = y$ ?

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Answer 1 · 2017-04-03T21:05:55

$ln 432 \approx 6.0684$ $ln 432 ~~ 6.0684$

Explanation:

Suppose you know:

$log 2 \approx 0.30103$ $log 2 ~~ 0.30103$

$log 3 \approx 0.47712$ $log 3 ~~ 0.47712$

$ln 10 \approx 2.302585$ $ln 10 ~~ 2.302585$

Then:

$\frac{ln 432}{ln 10} = log 432 = log (2^{4} 3^{3}) = 4 log 2 + 3 log 3$ $(ln 432)/(ln 10) = log 432 = log (2^4 3^3) = 4 log 2 + 3 log 3$

So:

$ln 432 = (ln 10) (4 log 2 + 3 log 3)$ $ln 432 = (ln 10)(4 log 2 + 3 log 3)$

$ln 432 \approx 2.302585 \cdot (4 \cdot 0.30103 + 3 \cdot 0.47712)$ $color(white)(ln 432) ~~ 2.302585*(4*0.30103 + 3*0.47712)$

$ln 432 \approx 6.0684$ $color(white)(ln 432) ~~ 6.0684$

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How do you evaluate $ln 432 = y$ $Ln 432 = y$ ?

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