What is simplify-log_{10}(5*10^8) ?

The solution to simplify-log_{10}(5*10^8) is -log_{10}(5)-8

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simplify-log_{10}(5*10^8)

simplify

- lo g_{10} (5 \cdot 1 0^{8})

- lo g_{10} (5) - 8

Decimal Notation

- 8.69897 \dots

Solution steps

- lo g_{10} (5 \cdot 1 0^{8})

Apply log rule:

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

lo g_{10} (5 \cdot 1 0^{8}) = lo g_{10} (5) + lo g_{10} (1 0^{8})

= - (lo g_{10} (5) + lo g_{10} (1 0^{8}))

Apply log rule:

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

lo g_{10} (1 0^{8}) = 8 lo g_{10} (10)

= - (lo g_{10} (5) + 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= - (lo g_{10} (5) + 8)

Distribute parentheses

= - (lo g_{10} (5)) - (8)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (5) - 8

ln \frac{( x ( x ^{2} + 1 ) ^{2} )}{2 x ^{3} - 1}

4 \cdot ln (- 1) + ln (4)

lo g_{e} (5 x^{- 6})

\frac{1}{3} ln ∣ 3 \cdot 2 - 2 ∣ - \frac{1}{3} ln ∣ 5 ∣

ln (\frac{1}{2} e^{iπ})

What is simplify-log_{10}(5*10^8) ?
The solution to simplify-log_{10}(5*10^8) is -log_{10}(5)-8