What is simplify-log_{10}(2*10^{-1}) ?

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

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simplify-log_{10}(2*10^{-1})

simplify

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

- lo g_{10} (2) + 1

Decimal Notation

0.69897 \dots

Solution steps

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

Apply log rule:

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

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

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

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

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

Distribute parentheses

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

Apply minus-plus rules

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

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

4 lo g_{5} (x) - 3 lo g_{5} (y)

0.026 ln (0.095) + 0.416 ln (10)

- ln (\frac{1}{2})

lo g_{2} (3) + 4 lo g_{2} (x) - 2 lo g_{2} (y)

lo g_{10} (a) + 2 lo g_{10} (b) - 3 lo g_{10} (c)

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