What is 5log_{10}(k)-log_{10}(q) ?

The solution to 5log_{10}(k)-log_{10}(q) is log_{10}((k^5)/q)

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simplify 5log_{10}(k)-log_{10}(q)

simplify

5 lo g_{10} (k) - lo g_{10} (q)

lo g_{10} (\frac{k ^{5}}{q})

Solution steps

5 lo g_{10} (k) - lo g_{10} (q)

Apply log rule:

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

5 lo g_{10} (k) = lo g_{10} (k^{5})

= lo g_{10} (k^{5}) - lo g_{10} (q)

Apply log rule:

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

lo g_{10} (k^{5}) - lo g_{10} (q) = lo g_{10} (\frac{k ^{5}}{q})

= lo g_{10} (\frac{k ^{5}}{q})

lo g_{10} (\frac{a ^{5} b ^{7}}{c ^{2}})

ln (x^{5} - 1) - ln (x^{3} - 1)

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

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

lo g_{10} (\frac{2 x ^{3} + 4}{5 x ^{3} - x})

What is 5log_{10}(k)-log_{10}(q) ?
The solution to 5log_{10}(k)-log_{10}(q) is log_{10}((k^5)/q)