What is simplify-log_{10}(4*10^{-1}) ?

The solution to simplify-log_{10}(4*10^{-1}) is -2log_{10}(2)+1

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simplify-log_{10}(4*10^{-1})

simplify

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

- 2 lo g_{10} (2) + 1

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= - (lo g_{10} (4) - 1 \cdot lo g_{10} (10))

1 \cdot lo g_{10} (10) = 1

= - (lo g_{10} (4) - 1)

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

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

Distribute parentheses

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

Apply minus-plus rules

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

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

ln (2) + 2 ln (2)

ln (n) + ln (v^{3})

(1) ln (18 (1)) - 1

ln (16) - ln (3) - ln (5)

ln (\frac{250}{6})

What is simplify-log_{10}(4*10^{-1}) ?
The solution to simplify-log_{10}(4*10^{-1}) is -2log_{10}(2)+1