What is simplify-log_{10}(2.3x10^{-10}) ?

The solution to simplify-log_{10}(2.3x10^{-10}) is -log_{10}(2.3)-log_{10}(x)+10

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simplify-log_{10}(2.3x10^{-10})

simplify

- lo g_{10} (2.3 x 1 0^{- 10})

- lo g_{10} (2.3) - lo g_{10} (x) + 10

Solution steps

- lo g_{10} (2.3 x \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (2.3 x \cdot 1 0^{- 10}) = lo g_{10} (2.3) + lo g_{10} (x) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (x) + lo g_{10} (2.3) + 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} (2.3) + lo g_{10} (x) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (x) + lo g_{10} (2.3) - 10)

Distribute parentheses

= - (lo g_{10} (2.3)) - (lo g_{10} (x)) - (- 10)

Apply minus-plus rules

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

= - lo g_{10} (2.3) - lo g_{10} (x) + 10

ln (2 x^{4}) + ln (3 x^{5})

ln (w) + 2 ln (y)

lo g_{3} (- x) - lo g_{3} (2) + 2

\frac{( 6 ln ( x + 9 ) + ln ( x ) - 2 ln ( x ) )}{2}

ln (\frac{3 z + 2 i}{4 z - 5 i})

What is simplify-log_{10}(2.3x10^{-10}) ?
The solution to simplify-log_{10}(2.3x10^{-10}) is -log_{10}(2.3)-log_{10}(x)+10