What is log_{10}(6)+4log_{10}(2) ?

The solution to log_{10}(6)+4log_{10}(2) is log_{10}(96)

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simplify log_{10}(6)+4log_{10}(2)

simplify

lo g_{10} (6) + 4 lo g_{10} (2)

lo g_{10} (96)

Decimal Notation

1.98227 \dots

Solution steps

lo g_{10} (6) + 4 lo g_{10} (2)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

4 lo g_{10} (2) = lo g_{10} (2^{4})

= lo g_{10} (6) + lo g_{10} (2^{4})

Apply log rule:

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

lo g_{10} (6) + lo g_{10} (2^{4}) = lo g_{10} (6 \cdot 2^{4})

= lo g_{10} (6 \cdot 2^{4})

6 \cdot 2^{4} = 96

= lo g_{10} (96)

- lo g_{10} (1 x 1 0^{- 7})

\frac{1}{4} lo g_{c} (x) + 5 lo g_{c} (y) - 4 lo g_{c} (x)

ln (y \frac{y}{4 - y})

lo g_{9} (x + 3) + lo g_{9} (x - 5)

\frac{1}{2} ln (- 1)

What is log_{10}(6)+4log_{10}(2) ?
The solution to log_{10}(6)+4log_{10}(2) is log_{10}(96)