What is simplify-log_{10}(4.4*10^{-6}) ?

The solution to simplify-log_{10}(4.4*10^{-6}) is -log_{10}(4.4)+6

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simplify-log_{10}(4.4*10^{-6})

simplify

- lo g_{10} (4.4 \cdot 1 0^{- 6})

- lo g_{10} (4.4) + 6

Decimal Notation

5.35654 \dots

Solution steps

- lo g_{10} (4.4 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (4.4 \cdot 1 0^{- 6}) = lo g_{10} (4.4) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (4.4) + lo g_{10} (1 0^{- 6}))

Apply log rule:

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

lo g_{10} (1 0^{- 6}) = - 6 lo g_{10} (10)

= - (lo g_{10} (4.4) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (4.4) - 6)

Distribute parentheses

= - (lo g_{10} (4.4)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (4.4) + 6

ln (\frac{25}{8})

- \frac{3}{8} \cdot lo g_{2} (\frac{3}{8}) - \frac{5}{8} lo g_{2} (\frac{5}{8})

ln (3 x^{2} y^{3})

ln (7.9) - ln (7.5)

ln (x^{6} \frac{y ^{15}}{z ^{16}})

What is simplify-log_{10}(4.4*10^{-6}) ?
The solution to simplify-log_{10}(4.4*10^{-6}) is -log_{10}(4.4)+6