What is 3/28 ln|15|-3/28 ln|8| ?

The solution to 3/28 ln|15|-3/28 ln|8| is 1/28 ln(3375/512)

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simplify 3/28 ln|15|-3/28 ln|8|

simplify

\frac{3}{28} ln ∣ 15 ∣ - \frac{3}{28} ln ∣ 8 ∣

\frac{1}{28} ln (\frac{3375}{512})

Decimal Notation

0.06735 \dots

Solution steps

\frac{3}{28} ln ∣ 15 ∣ - \frac{3}{28} ln ∣ 8 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{3}{28} ln ∣ 15 ∣ = ln (∣ 15 ∣^{\frac{3}{28}})

= ln (∣ 15 ∣^{\frac{3}{28}}) - \frac{3}{28} ln ∣ 8 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{3}{28} ln ∣ 8 ∣ = ln (∣ 8 ∣^{\frac{3}{28}})

= ln (∣ 15 ∣^{\frac{3}{28}}) - ln (∣ 8 ∣^{\frac{3}{28}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (∣ 15 ∣^{\frac{3}{28}}) - ln (∣ 8 ∣^{\frac{3}{28}}) = ln (\frac{∣ 15 ∣ ^{\frac{3}{28}}}{∣ 8 ∣ ^{\frac{3}{28}}})

= ln (\frac{∣ 15 ∣ ^{\frac{3}{28}}}{∣ 8 ∣ ^{\frac{3}{28}}})

Rewrite as

= ln ((\frac{3375}{512})^{\frac{1}{28}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{28} ln (\frac{3375}{512})

- \frac{1}{12} ln ∣ y ∣ + \frac{1}{12} ln ∣ y - 3 ∣

ln (4 a^{(3)} b^{(5)})

4 lo g_{10} (x + 6) - lo g_{10} (x)

ln (\frac{4 x}{2 + x ^{2}})

- lo g_{10} (1.07 \cdot 1 0^{- 6})

What is 3/28 ln|15|-3/28 ln|8| ?
The solution to 3/28 ln|15|-3/28 ln|8| is 1/28 ln(3375/512)