What is log_{10}(5*e^9) ?

The solution to log_{10}(5*e^9) is log_{10}(5)+9log_{10}(e)

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simplify log_{10}(5*e^9)

simplify

lo g_{10} (5 \cdot e^{9})

lo g_{10} (5) + 9 lo g_{10} (e)

Decimal Notation

4.60762 \dots

Solution steps

lo g_{10} (5 e^{9})

Apply log rule:

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

lo g_{10} (5 e^{9}) = lo g_{10} (5) + lo g_{10} (e^{9})

= lo g_{10} (5) + lo g_{10} (e^{9})

Apply log rule:

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

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

= lo g_{10} (5) + 9 lo g_{10} (e)

ln (\frac{3}{3 - x})

ln (\frac{15}{13})

lo g_{10} (7) + 2 lo g_{10} (x) - 5 lo g_{10} (y)

\frac{1}{2} lo g_{7} (r - 1) - \frac{1}{2} lo g_{7} (r)

lo g_{10} (3.2 \cdot e^{- 5})

What is log_{10}(5*e^9) ?
The solution to log_{10}(5*e^9) is log_{10}(5)+9log_{10}(e)