What is log_{10}(a^5b^4) ?

The solution to log_{10}(a^5b^4) is 5log_{10}(a)+4log_{10}(b)

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simplify log_{10}(a^5b^4)

simplify

lo g_{10} (a^{5} b^{4})

5 lo g_{10} (a) + 4 lo g_{10} (b)

Solution steps

lo g_{10} (a^{5} b^{4})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (a^{5} b^{4}) = lo g_{10} (a^{5}) + lo g_{10} (b^{4})

= lo g_{10} (a^{5}) + lo g_{10} (b^{4})

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

lo g_{10} (b^{4}) = 4 lo g_{10} (b)

= 5 lo g_{10} (a) + 4 lo g_{10} (b)

lo g_{10} (\frac{( x ^{2} y )}{( w ^{5} z )})

lo g_{b} (\frac{x}{( yz ) ^{2}})

- lo g_{10} (3 \cdot 1 0^{- 5})

lo g_{4} (\frac{1}{8}) \cdot lo g_{8} (256)

ln (x + 4) - 3 ln (x) - ln (y)

What is log_{10}(a^5b^4) ?
The solution to log_{10}(a^5b^4) is 5log_{10}(a)+4log_{10}(b)