What is 0.2ln(30)+0.8ln(5) ?

The solution to 0.2ln(30)+0.8ln(5) is ln(7.15484…)

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simplify 0.2ln(30)+0.8ln(5)

simplify

0.2 ln (30) + 0.8 ln (5)

ln (7.15484 \dots)

Decimal Notation

1.96778 \dots

Solution steps

0.2 ln (30) + 0.8 ln (5)

Apply log rule:

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

0.2 ln (30) = ln (3 0^{0.2})

= ln (3 0^{0.2}) + 0.8 ln (5)

Apply log rule:

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

0.8 ln (5) = ln (5^{0.8})

= ln (3 0^{0.2}) + ln (5^{0.8})

Apply log rule:

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

ln (3 0^{0.2}) + ln (5^{0.8}) = ln (3 0^{0.2} \cdot 5^{0.8})

= ln (3 0^{0.2} \cdot 5^{0.8})

3 0^{0.2} \cdot 5^{0.8} = 7.15484 \dots

= ln (7.15484 \dots)

- \frac{( 1 )}{( 2 )} ln^{4} (x^{2}) - \frac{( 1 )}{( 2 )} ln (x^{2})

lo g_{5} ((\frac{x}{2 y})^{8})

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\frac{ln ( 5.999 ) - ln ( 6 )}{5.999 - 6}