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

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

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simplify 3log_{10}(a)-log_{10}(q)

simplify

3 lo g_{10} (a) - lo g_{10} (q)

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

Solution steps

3 lo g_{10} (a) - lo g_{10} (q)

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}) - lo g_{10} (q)

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

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

ln (x^{2} - 9) + 2 ln (\frac{1}{x + 3}) + 4 ln (x)

lo g_{10} (w^{6} u \cdot v)

2 ln (a) - ln (b)

lo g_{10} (500) - lo g_{10} (2)

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