What is simplify-log_{10}(2.1*10^{-10}) ?

The solution to simplify-log_{10}(2.1*10^{-10}) is -log_{10}(2.1)+10

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simplify-log_{10}(2.1*10^{-10})

simplify

- lo g_{10} (2.1 \cdot 1 0^{- 10})

- lo g_{10} (2.1) + 10

Decimal Notation

9.67778 \dots

Solution steps

- lo g_{10} (2.1 \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (2.1 \cdot 1 0^{- 10}) = lo g_{10} (2.1) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (2.1) + 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} (2.1) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (2.1) - 10)

Distribute parentheses

= - (lo g_{10} (2.1)) - (- 10)

Apply minus-plus rules

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

= - lo g_{10} (2.1) + 10

ln (\frac{10}{16})

2.49 - \frac{0.0592}{1} \cdot lo g_{10} (\frac{0.35}{0.25})

lo g_{10} (\frac{4 x ^{2}}{( 3 x y ) ^{5}})

\frac{1}{3} ln (x) + \frac{10}{12} ln (x + 3) - \frac{1}{6} ln (x - 3)

What is simplify-log_{10}(2.1*10^{-10}) ?
The solution to simplify-log_{10}(2.1*10^{-10}) is -log_{10}(2.1)+10