How do you simplify $ln 3 - 2 ln 8 + ln 16$ $ln 3 − 2 ln 8 + ln 16$ ?

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How do you simplify $ln 3 - 2 ln 8 + ln 16$ $ln 3 − 2 ln 8 + ln 16$ ?

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Answer 1 · 2018-03-25T12:40:31

$ln (\frac{3}{4})$ $ln(3/4)$

Explanation:

We have to use the Logarithm Properties.

$ln (3) - 2 ln (8) + ln (16)$ $ln(3)-2ln(8)+ln(16)$

We can rewrite the initial expression using the Power rule in this way
$ln (3) - ln (8^{2}) + ln (16)$ $ln(3)-ln(8^2)+ln(16)$

$ln (3) - ln (64) + ln (16)$ $ln(3)-ln(64)+ln(16)$

Here we use the Quotient rule
$ln (\frac{3}{64}) + ln (16)$ $ln(3/64)+ln(16)$

And here the Product rule
$ln (\frac{3}{64} \cdot 16)$ $ln(3/64*16)$

$ln (\frac{48}{64})$ $ln(48/64)$

Finally we get the semplified version :
$ln (\frac{3}{4})$ $ln(3/4)$

Answer 2 · 2018-03-25T12:47:38

$ln (\frac{3}{4})$ $ln(3/4)$

Explanation:

$using the laws of logarithms$ $"using the "color(blue)"laws of logarithms"$

$∙ x {log x}^{n} \Leftrightarrow n log x$ $•color(white)(x)logx^nhArrnlogx$

$∙ x log x + log y \Leftrightarrow log (x y)$ $•color(white)(x)logx+logyhArrlog(xy)$

$∙ x log x - log y \Leftrightarrow log (\frac{x}{y})$ $•color(white)(x)logx-logyhArrlog(x/y)$

$\Rightarrow ln 3 - {ln 8}^{2} + ln 16$ $rArrln3-ln8^2+ln16$

$= ln (\frac{3 \times 16}{64}) = ln (\frac{48}{64}) = ln (\frac{3}{4})$ $=ln((3xx16)/64)=ln(48/64)=ln(3/4)$

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How do you simplify $ln 3 - 2 ln 8 + ln 16$ $ln 3 − 2 ln 8 + ln 16$ ?

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How do you simplify ln3−2ln8+ln16ln 3 − 2 ln 8 + ln 16?

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How do you simplify $ln 3 - 2 ln 8 + ln 16$ $ln 3 − 2 ln 8 + ln 16$ ?