What is simplify-log_{10}(2.1*10^{-53}) ?

The solution to simplify-log_{10}(2.1*10^{-53}) is -log_{10}(2.1)+53

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simplify-log_{10}(2.1*10^{-53})

simplify

- lo g_{10} (2.1 \cdot 1 0^{- 53})

- lo g_{10} (2.1) + 53

Decimal Notation

52.67778 \dots

Solution steps

- lo g_{10} (2.1 \cdot 1 0^{- 53})

Apply log rule:

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

lo g_{10} (2.1 \cdot 1 0^{- 53}) = lo g_{10} (2.1) + lo g_{10} (1 0^{- 53})

= - (lo g_{10} (2.1) + lo g_{10} (1 0^{- 53}))

Apply log rule:

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

lo g_{10} (1 0^{- 53}) = - 53 lo g_{10} (10)

= - (lo g_{10} (2.1) - 53 lo g_{10} (10))

53 lo g_{10} (10) = 53

= - (lo g_{10} (2.1) - 53)

Distribute parentheses

= - (lo g_{10} (2.1)) - (- 53)

Apply minus-plus rules

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

= - lo g_{10} (2.1) + 53

ln (1.6296 \cdot π)

lo g_{e} (6 x^{2} - 2) - lo g_{e} (x^{2})

\frac{1}{3} ln (2 x + 1) + \frac{1}{2} [ln (x - 4) - ln (x^{2} + 5)]

- lo g_{10} (5 (1 0^{- 2}))

ln (1 + n^{2}) - ln (n)

What is simplify-log_{10}(2.1*10^{-53}) ?
The solution to simplify-log_{10}(2.1*10^{-53}) is -log_{10}(2.1)+53