What is simplify-log_{10}(1.8*10^{-15}) ?

The solution to simplify-log_{10}(1.8*10^{-15}) is -log_{10}(1.8)+15

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simplify-log_{10}(1.8*10^{-15})

simplify

- lo g_{10} (1.8 \cdot 1 0^{- 15})

- lo g_{10} (1.8) + 15

Decimal Notation

14.74472 \dots

Solution steps

- lo g_{10} (1.8 \cdot 1 0^{- 15})

Apply log rule:

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

lo g_{10} (1.8 \cdot 1 0^{- 15}) = lo g_{10} (1.8) + lo g_{10} (1 0^{- 15})

= - (lo g_{10} (1.8) + lo g_{10} (1 0^{- 15}))

Apply log rule:

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

lo g_{10} (1 0^{- 15}) = - 15 lo g_{10} (10)

= - (lo g_{10} (1.8) - 15 lo g_{10} (10))

15 lo g_{10} (10) = 15

= - (lo g_{10} (1.8) - 15)

Distribute parentheses

= - (lo g_{10} (1.8)) - (- 15)

Apply minus-plus rules

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

= - lo g_{10} (1.8) + 15

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What is simplify-log_{10}(1.8*10^{-15}) ?
The solution to simplify-log_{10}(1.8*10^{-15}) is -log_{10}(1.8)+15