What is (1.6)/2 ln(10)-1.6ln(3) ?

The solution to (1.6)/2 ln(10)-1.6ln(3) is ln(1.08794…)

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simplify (1.6)/2 ln(10)-1.6ln(3)

simplify

\frac{1.6}{2} ln (10) - 1.6 ln (3)

ln (1.08794 \dots)

Decimal Notation

0.08428 \dots

Solution steps

\frac{1.6}{2} ln (10) - 1.6 ln (3)

Apply log rule:

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

\frac{1.6}{2} ln (10) = ln (1 0^{\frac{1.6}{2}})

= ln (1 0^{\frac{1.6}{2}}) - 1.6 ln (3)

Apply log rule:

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

1.6 ln (3) = ln (3^{1.6})

= ln (1 0^{\frac{1.6}{2}}) - ln (3^{1.6})

Apply log rule:

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

ln (1 0^{\frac{1.6}{2}}) - ln (3^{1.6}) = ln (\frac{1 0 ^{\frac{1.6}{2}}}{3 ^{1.6}})

= ln (\frac{1 0 ^{\frac{1.6}{2}}}{3 ^{1.6}})

\frac{1 0 ^{\frac{1.6}{2}}}{3 ^{1.6}} = 1.08794 \dots

= ln (1.08794 \dots)

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What is (1.6)/2 ln(10)-1.6ln(3) ?
The solution to (1.6)/2 ln(10)-1.6ln(3) is ln(1.08794…)