What is simplify-log_{10}(4.7*10^{-4}) ?

The solution to simplify-log_{10}(4.7*10^{-4}) is -log_{10}(4.7)+4

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simplify-log_{10}(4.7*10^{-4})

simplify

- lo g_{10} (4.7 \cdot 1 0^{- 4})

- lo g_{10} (4.7) + 4

Decimal Notation

3.32790 \dots

Solution steps

- lo g_{10} (4.7 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (4.7 \cdot 1 0^{- 4}) = lo g_{10} (4.7) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (4.7) + 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} (4.7) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (4.7) - 4)

Distribute parentheses

= - (lo g_{10} (4.7)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (4.7) + 4

lo g_{4} (x) + lo g_{4} (x) - 1.5

ln (\frac{6}{13})

- lo g_{10} (\frac{0.00001 - 0.00001}{2})

ln ((\frac{1}{( 2 x )}) e^{\frac{- ∣ a ∣}{x}})

2 lo g_{b} (z) + 3 (lo g_{b} (x) - 4 lo g_{b} (w))

What is simplify-log_{10}(4.7*10^{-4}) ?
The solution to simplify-log_{10}(4.7*10^{-4}) is -log_{10}(4.7)+4