What is simplify-log_{10}(1.25(10^{-4})) ?

The solution to simplify-log_{10}(1.25(10^{-4})) is -log_{10}(1.25)+4

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simplify-log_{10}(1.25(10^{-4}))

simplify

- lo g_{10} (1.25 (1 0^{- 4}))

- lo g_{10} (1.25) + 4

Decimal Notation

3.90308 \dots

Solution steps

- lo g_{10} (1.25 (1 0^{- 4}))

Apply log rule:

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

lo g_{10} (1.25 (1 0^{- 4})) = lo g_{10} (1.25) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (1.25) + lo g_{10} (1 0^{- 4}))

Apply log rule:

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

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

= - (lo g_{10} (1.25) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (1.25) - 4)

Distribute parentheses

= - (lo g_{10} (1.25)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (1.25) + 4

- lo g_{10} ((1.8 \cdot 1 0^{- 5}) (1))

ln (6 e^{m})

- \frac{1}{2} ln (\frac{1}{16}) + ln (\frac{1}{2})

ln (x^{4} y^{3})

(\frac{1}{0.143}) ln (\frac{5 x 1 0 ^{9}}{34000})

What is simplify-log_{10}(1.25(10^{-4})) ?
The solution to simplify-log_{10}(1.25(10^{-4})) is -log_{10}(1.25)+4