What is log_{10}(a)-7log_{10}(b) ?

The solution to log_{10}(a)-7log_{10}(b) is log_{10}(a/(b^7))

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simplify log_{10}(a)-7log_{10}(b)

simplify

lo g_{10} (a) - 7 lo g_{10} (b)

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

Solution steps

lo g_{10} (a) - 7 lo g_{10} (b)

Apply log rule:

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

7 lo g_{10} (b) = lo g_{10} (b^{7})

= lo g_{10} (a) - lo g_{10} (b^{7})

Apply log rule:

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

lo g_{10} (a) - lo g_{10} (b^{7}) = lo g_{10} (\frac{a}{b ^{7}})

= lo g_{10} (\frac{a}{b ^{7}})

lo g_{10} (2 x^{3})

ln (1 + y) - ln (y)

ln (7) - ln (3)

- ln (x) + ln (y)

10 ln (3 x) - (ln (3 x))^{2}

What is log_{10}(a)-7log_{10}(b) ?
The solution to log_{10}(a)-7log_{10}(b) is log_{10}(a/(b^7))