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

The solution to 3log_{10}(a)-2log_{10}(k) is log_{10}((a^3)/(k^2))

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simplify 3log_{10}(a)-2log_{10}(k)

simplify

3 lo g_{10} (a) - 2 lo g_{10} (k)

lo g_{10} (\frac{a ^{3}}{k ^{2}})

Solution steps

3 lo g_{10} (a) - 2 lo g_{10} (k)

Apply log rule:

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

3 lo g_{10} (a) = lo g_{10} (a^{3})

= lo g_{10} (a^{3}) - 2 lo g_{10} (k)

Apply log rule:

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

2 lo g_{10} (k) = lo g_{10} (k^{2})

= lo g_{10} (a^{3}) - lo g_{10} (k^{2})

Apply log rule:

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

lo g_{10} (a^{3}) - lo g_{10} (k^{2}) = lo g_{10} (\frac{a ^{3}}{k ^{2}})

= lo g_{10} (\frac{a ^{3}}{k ^{2}})

2 lo g_{10} (x) + \frac{1}{2} lo g_{10} (y)

ln (7) - 2 ln (2)

4 ln (\frac{16}{21})

lo g_{3} (\frac{3}{2}) + lo g_{3} (4.5)

\frac{1}{2} lo g_{10} (x) - lo g_{10} (3 y)

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