What is log_{10}(a^6b^4) ?

The solution to log_{10}(a^6b^4) is 6log_{10}(a)+4log_{10}(b)

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simplify log_{10}(a^6b^4)

simplify

lo g_{10} (a^{6} b^{4})

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

Solution steps

lo g_{10} (a^{6} b^{4})

Apply log rule:

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

lo g_{10} (a^{6} b^{4}) = lo g_{10} (a^{6}) + lo g_{10} (b^{4})

= lo g_{10} (a^{6}) + lo g_{10} (b^{4})

lo g_{10} (a^{6}) = 6 lo g_{10} (a)

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

= 6 lo g_{10} (a) + 4 lo g_{10} (b)

3 ln (2) + 2 ln (x) - 12 ln (x + 4)

3 lo g_{2} (x) + lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{5} (1000) + lo g_{4 a} (64 a^{3})

lo g_{3^{x}} (+ 2 lo g_{3^{y} - l o g_{3^{z}} (x)} (x))

ln (\frac{e ^{- x} - e ^{x}}{e ^{x} + e ^{- x}})

What is log_{10}(a^6b^4) ?
The solution to log_{10}(a^6b^4) is 6log_{10}(a)+4log_{10}(b)