What is simplify-log_{10}(2.7*10^{-11}) ?

The solution to simplify-log_{10}(2.7*10^{-11}) is -log_{10}(2.7)+11

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simplify-log_{10}(2.7*10^{-11})

simplify

- lo g_{10} (2.7 \cdot 1 0^{- 11})

- lo g_{10} (2.7) + 11

Decimal Notation

10.56863 \dots

Solution steps

- lo g_{10} (2.7 \cdot 1 0^{- 11})

Apply log rule:

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

lo g_{10} (2.7 \cdot 1 0^{- 11}) = lo g_{10} (2.7) + lo g_{10} (1 0^{- 11})

= - (lo g_{10} (2.7) + lo g_{10} (1 0^{- 11}))

Apply log rule:

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

lo g_{10} (1 0^{- 11}) = - 11 lo g_{10} (10)

= - (lo g_{10} (2.7) - 11 lo g_{10} (10))

11 lo g_{10} (10) = 11

= - (lo g_{10} (2.7) - 11)

Distribute parentheses

= - (lo g_{10} (2.7)) - (- 11)

Apply minus-plus rules

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

= - lo g_{10} (2.7) + 11

lo g_{5} (- 1.55 + 3) + lo g_{5} (- 1.55 + 5)

lo g_{10} (\frac{( m - n ) ( m + n )}{( m - n ) ^{2}})

(\frac{1}{2}) ln (4 t^{4}) - ln (2)

- lo g_{10} (2.5 \cdot 1 0^{- 1})

3 ln (2 x^{3})

What is simplify-log_{10}(2.7*10^{-11}) ?
The solution to simplify-log_{10}(2.7*10^{-11}) is -log_{10}(2.7)+11