What is simplify-log_{10}(4*10^{-2}) ?

The solution to simplify-log_{10}(4*10^{-2}) is -2log_{10}(2)+2

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simplify-log_{10}(4*10^{-2})

simplify

- lo g_{10} (4 \cdot 1 0^{- 2})

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

Decimal Notation

1.39794 \dots

Solution steps

- lo g_{10} (4 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 2}) = lo g_{10} (4) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (4) + 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} (4) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (4) - 2)

lo g_{10} (4) = 2 lo g_{10} (2)

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

Distribute parentheses

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

Apply minus-plus rules

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

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

lo g_{b} (x y) + lo g_{b} (x z) - lo g_{b} (\frac{x}{yz})

2 lo g_{10} (x) - (3 lo g_{10} (y) + 2 lo g_{10} (z))

ln (x) + 2 ln (y) - ln (z)

- 2 ln (3) + 2 ln (2)

What is simplify-log_{10}(4*10^{-2}) ?
The solution to simplify-log_{10}(4*10^{-2}) is -2log_{10}(2)+2