What is simplify-log_{10}(8*10^{-2}) ?

The solution to simplify-log_{10}(8*10^{-2}) is -3log_{10}(2)+2

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simplify-log_{10}(8*10^{-2})

simplify

- lo g_{10} (8 \cdot 1 0^{- 2})

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

Decimal Notation

1.09691 \dots

Solution steps

- lo g_{10} (8 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (8 \cdot 1 0^{- 2}) = lo g_{10} (8) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (8) + 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} (8) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (8) - 2)

lo g_{10} (8) = 3 lo g_{10} (2)

= - (3 lo g_{10} (2) - 2)

Distribute parentheses

= - (3 lo g_{10} (2)) - (- 2)

Apply minus-plus rules

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

= - 3 lo g_{10} (2) + 2

ln (x - 1) + ln (4 x - 1)

- lo g_{10} (2.5 x 1 0^{- 4})

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What is simplify-log_{10}(8*10^{-2}) ?
The solution to simplify-log_{10}(8*10^{-2}) is -3log_{10}(2)+2