What is 0.04+0.36ln(2)+0.57ln(5) ?

The solution to 0.04+0.36ln(2)+0.57ln(5) is 0.04+ln(3.21206…)

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simplify 0.04+0.36ln(2)+0.57ln(5)

simplify

0.04 + 0.36 ln (2) + 0.57 ln (5)

0.04 + ln (3.21206 \dots)

Decimal Notation

1.20691 \dots

Solution steps

0.04 + 0.36 ln (2) + 0.57 ln (5)

Apply log rule:

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

0.36 ln (2) = ln (2^{0.36})

= 0.04 + ln (2^{0.36}) + 0.57 ln (5)

Apply log rule:

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

0.57 ln (5) = ln (5^{0.57})

= 0.04 + ln (2^{0.36}) + ln (5^{0.57})

Apply log rule:

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

ln (2^{0.36}) + ln (5^{0.57}) = ln (2^{0.36} \cdot 5^{0.57})

= 0.04 + ln (2^{0.36} \cdot 5^{0.57})

2^{0.36} \cdot 5^{0.57} = 3.21206 \dots

= 0.04 + ln (3.21206 \dots)

lo g_{10} (3 x y^{3})

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

lo g_{10} (\frac{z y}{x ^{2}})

- lo g_{10} (6 \cdot 1 0^{- 2})

- lo g_{10} (2.2 \cdot 1 0^{- 7})

What is 0.04+0.36ln(2)+0.57ln(5) ?
The solution to 0.04+0.36ln(2)+0.57ln(5) is 0.04+ln(3.21206…)