What is simplify-log_{10}(5(10^{-2})) ?

The solution to simplify-log_{10}(5(10^{-2})) is -log_{10}(5)+2

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simplify-log_{10}(5(10^{-2}))

simplify

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

- lo g_{10} (5) + 2

Decimal Notation

1.30102 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= - (lo g_{10} (5) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (5) - 2)

Distribute parentheses

= - (lo g_{10} (5)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (5) + 2

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

ln (\frac{1643.85}{821.85}) \cdot 8

ln - \frac{m g}{b} + a - ln (\frac{∣ m ∣ ∣ g ∣}{∣ b ∣})

- lo g_{10} (2.92 \cdot 1 0^{- 14})

\frac{3}{2} ln ∣ (- 0.5 - 1) ∣ - \frac{3}{2} ln ∣ (- 1 - 1) ∣

What is simplify-log_{10}(5(10^{-2})) ?
The solution to simplify-log_{10}(5(10^{-2})) is -log_{10}(5)+2