What is 5ln(2)-1/2+5ln(3) ?

The solution to 5ln(2)-1/2+5ln(3) is 5ln(6)-1/2

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simplify 5ln(2)-1/2+5ln(3)

simplify

5 ln (2) - \frac{1}{2} + 5 ln (3)

5 ln (6) - \frac{1}{2}

Decimal Notation

8.45879 \dots

Solution steps

5 ln (2) - \frac{1}{2} + 5 ln (3)

Apply log rule:

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

5 ln (2) = ln (2^{5})

= ln (2^{5}) - \frac{1}{2} + 5 ln (3)

Apply log rule:

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

5 ln (3) = ln (3^{5})

= ln (2^{5}) - \frac{1}{2} + ln (3^{5})

Apply log rule:

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

ln (2^{5}) + ln (3^{5}) = ln (2^{5} \cdot 3^{5})

= ln (2^{5} \cdot 3^{5}) - \frac{1}{2}

2^{5} \cdot 3^{5} = 7776

= ln (7776) - \frac{1}{2}

ln (7776) = 5 ln (6)

= 5 ln (6) - \frac{1}{2}

lo g_{4} (\frac{x ^{2}}{yz})

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\frac{1}{2} lo g_{b} (x) + 3 lo g_{b} (y) - 5 lo g_{b} (x)

lo g_{5} (\frac{8}{x})