What is ln|7-2|-3/2 ln|2*7-1|+2ln|7+3|+4.83 ?

The solution to ln|7-2|-3/2 ln|2*7-1|+2ln|7+3|+4.83 is ln((500sqrt(13))/(169))+4.83

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simplify ln|7-2|-3/2 ln|2*7-1|+2ln|7+3|+4.83

simplify

ln ∣ 7 - 2 ∣ - \frac{3}{2} ln ∣ 2 \cdot 7 - 1 ∣ + 2 ln ∣ 7 + 3 ∣ + 4.83

ln (\frac{500 13}{169}) + 4.83

Decimal Notation

7.19718 \dots

Solution steps

ln ∣ 7 - 2 ∣ - \frac{3}{2} ln ∣ 2 \cdot 7 - 1 ∣ + 2 ln ∣ 7 + 3 ∣ + 4.83

Apply log rule:

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

\frac{3}{2} ln ∣ 2 \cdot 7 - 1 ∣ = ln (∣ 2 \cdot 7 - 1 ∣^{\frac{3}{2}})

= ln ∣ 7 - 2 ∣ - ln (∣ 2 \cdot 7 - 1 ∣^{\frac{3}{2}}) + 2 ln ∣ 7 + 3 ∣ + 4.83

Apply log rule:

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

ln ∣ 7 - 2 ∣ - ln (∣ 2 \cdot 7 - 1 ∣^{\frac{3}{2}}) = ln (\frac{∣ 7 - 2 ∣}{∣ 2 \cdot 7 - 1 ∣ ^{\frac{3}{2}}})

= ln (\frac{∣ 7 - 2 ∣}{∣ 2 \cdot 7 - 1 ∣ ^{\frac{3}{2}}}) + 2 ln ∣ 7 + 3 ∣ + 4.83

\frac{∣ 7 - 2 ∣}{∣ 2 \cdot 7 - 1 ∣ ^{\frac{3}{2}}} = \frac{5 13}{169}

= ln (\frac{5 13}{169}) + 2 ln ∣ 7 + 3 ∣ + 4.83

Apply log rule:

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

2 ln ∣ 7 + 3 ∣ = ln (∣ 7 + 3 ∣^{2})

= ln (\frac{5 13}{169}) + ln (∣ 7 + 3 ∣^{2}) + 4.83

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{5 13}{169}) + ln (∣ 7 + 3 ∣^{2}) = ln (\frac{5 13}{169} ∣ 7 + 3 ∣^{2})

= ln (\frac{5 13}{169} ∣ 7 + 3 ∣^{2}) + 4.83

\frac{5 13}{169} ∣ 7 + 3 ∣^{2} = \frac{500 13}{169}

= ln (\frac{500 13}{169}) + 4.83

lo g_{e} (\frac{1 0 ^{- 12}}{2})

lo g_{10} (x y^{7})

lo g_{b} (\frac{1}{21})

2 lo g_{4} (11) - 10 lo g_{4} (10)

3 ln (x) - ln (3 x) + ln (12 x^{2})

What is ln|7-2|-3/2 ln|2*7-1|+2ln|7+3|+4.83 ?
The solution to ln|7-2|-3/2 ln|2*7-1|+2ln|7+3|+4.83 is ln((500sqrt(13))/(169))+4.83