What is log_{10}(2)-log_{10}(3i) ?

The solution to log_{10}(2)-log_{10}(3i) is log_{10}(-(2i)/3)

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simplify log_{10}(2)-log_{10}(3i)

simplify

lo g_{10} (2) - lo g_{10} (3 i)

lo g_{10} (- \frac{2 i}{3})

Solution steps

lo g_{10} (2) - lo g_{10} (3 i)

Apply log rule:

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

lo g_{10} (2) - lo g_{10} (3 i) = lo g_{10} (\frac{2}{3 i})

= lo g_{10} (\frac{2}{3 i})

Simplify

\frac{2}{3 i} : - \frac{2 i}{3}

= lo g_{10} (- \frac{2 i}{3})

- 0.6 \cdot lo g_{2} (0.6) - 0.3 \cdot lo g_{2} (0.3)

- 4 \cdot ln (\frac{25}{13}) - 5 \cdot ln (\frac{25}{13})

ln (\frac{x}{( x ^{2} + 1 ) ^{\frac{1}{2}}}) + x

\frac{1}{2} ln (\frac{110}{125})

lo g_{8} (\frac{9 x ^{2}}{y ^{3}})

What is log_{10}(2)-log_{10}(3i) ?
The solution to log_{10}(2)-log_{10}(3i) is log_{10}(-(2i)/3)