What is ln(7)-(2/3)*ln(2)+ln(3) ?

The solution to ln(7)-(2/3)*ln(2)+ln(3) is ln((21\sqrt[3]{2})/2)

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simplify ln(7)-(2/3)*ln(2)+ln(3)

simplify

ln (7) - (\frac{2}{3}) \cdot ln (2) + ln (3)

Decimal Notation

2.58242 \dots

Solution steps

ln (7) - (\frac{2}{3}) ln (2) + ln (3)

Apply log rule:

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

(\frac{2}{3}) ln (2) = ln (2^{(\frac{2}{3})})

= ln (7) - ln (2^{(\frac{2}{3})}) + ln (3)

Apply log rule:

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

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

= ln (\frac{7}{2 ^{\frac{2}{3}}}) + ln (3)

Apply log rule:

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

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What is ln(7)-(2/3)*ln(2)+ln(3) ?
The solution to ln(7)-(2/3)*ln(2)+ln(3) is ln((21\sqrt[3]{2})/2)