What is log_{10}(a)+9log_{10}(b) ?

The solution to log_{10}(a)+9log_{10}(b) is log_{10}(ab^9)

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simplify log_{10}(a)+9log_{10}(b)

simplify

lo g_{10} (a) + 9 lo g_{10} (b)

lo g_{10} (a b^{9})

Solution steps

lo g_{10} (a) + 9 lo g_{10} (b)

Apply log rule:

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

9 lo g_{10} (b) = lo g_{10} (b^{9})

= lo g_{10} (a) + lo g_{10} (b^{9})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (a) + lo g_{10} (b^{9}) = lo g_{10} (a b^{9})

= lo g_{10} (a b^{9})

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What is log_{10}(a)+9log_{10}(b) ?
The solution to log_{10}(a)+9log_{10}(b) is log_{10}(ab^9)