What is simplify-log_{10}(2.4*10^{-8}) ?

The solution to simplify-log_{10}(2.4*10^{-8}) is -log_{10}(2.4)+8

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simplify-log_{10}(2.4*10^{-8})

simplify

- lo g_{10} (2.4 \cdot 1 0^{- 8})

- lo g_{10} (2.4) + 8

Decimal Notation

7.61978 \dots

Solution steps

- lo g_{10} (2.4 \cdot 1 0^{- 8})

Apply log rule:

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

lo g_{10} (2.4 \cdot 1 0^{- 8}) = lo g_{10} (2.4) + lo g_{10} (1 0^{- 8})

= - (lo g_{10} (2.4) + lo g_{10} (1 0^{- 8}))

Apply log rule:

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

lo g_{10} (1 0^{- 8}) = - 8 lo g_{10} (10)

= - (lo g_{10} (2.4) - 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= - (lo g_{10} (2.4) - 8)

Distribute parentheses

= - (lo g_{10} (2.4)) - (- 8)

Apply minus-plus rules

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

= - lo g_{10} (2.4) + 8

3 ln (4) + 4 ln (3) - 4 ln (3)

- lo g_{10} (1.34 \cdot 1 0^{- 6})

5 ln (3) - 2 ln (3) + 2 ln (4)

(\frac{1}{2})^{x} - \frac{1}{4} ln (\frac{1}{x}) + arcsin (x) - \frac{5}{4}

ln (13) - ln (21)

What is simplify-log_{10}(2.4*10^{-8}) ?
The solution to simplify-log_{10}(2.4*10^{-8}) is -log_{10}(2.4)+8