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

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

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simplify log_{10}(a)+4log_{10}(b)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- (\frac{3}{7}) lo g_{2} (\frac{3}{7}) - (\frac{4}{7}) lo g_{2} (\frac{4}{7})

2 ln (2) - ln (5)

ln (\frac{0.6}{0.4})

lo g_{2} (\frac{8 x ^{4}}{5})

4 ln (x) + 2 ln (y) - 6 ln (z)

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