What is simplify-log_{10}(5.6*10^{-10}) ?

The solution to simplify-log_{10}(5.6*10^{-10}) is -log_{10}(5.6)+10

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simplify-log_{10}(5.6*10^{-10})

simplify

- lo g_{10} (5.6 \cdot 1 0^{- 10})

- lo g_{10} (5.6) + 10

Decimal Notation

9.25181 \dots

Solution steps

- lo g_{10} (5.6 \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (5.6 \cdot 1 0^{- 10}) = lo g_{10} (5.6) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (5.6) + lo g_{10} (1 0^{- 10}))

Apply log rule:

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

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

= - (lo g_{10} (5.6) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (5.6) - 10)

Distribute parentheses

= - (lo g_{10} (5.6)) - (- 10)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (5.6) + 10

2 lo g_{10} (M) - 3 lo g_{10} (N)

ln (x) - ln (x + 5) - 5 ln (9)

lo g_{b} (\frac{x ( x + 2 ) ^{2}}{( x - 2 ) ^{4}})

2 lo g_{3} (x) + 3 lo g_{3} (y) - 4 lo g_{3} (z)

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

What is simplify-log_{10}(5.6*10^{-10}) ?
The solution to simplify-log_{10}(5.6*10^{-10}) is -log_{10}(5.6)+10