What is simplify-log_{10}(5.4*10^{-4}) ?

The solution to simplify-log_{10}(5.4*10^{-4}) is -log_{10}(5.4)+4

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simplify-log_{10}(5.4*10^{-4})

simplify

- lo g_{10} (5.4 \cdot 1 0^{- 4})

- lo g_{10} (5.4) + 4

Decimal Notation

3.26760 \dots

Solution steps

- lo g_{10} (5.4 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (5.4 \cdot 1 0^{- 4}) = lo g_{10} (5.4) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (5.4) + 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} (5.4) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (5.4) - 4)

Distribute parentheses

= - (lo g_{10} (5.4)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (5.4) + 4

ln (2 + e^{1}) - ln (2 + e^{- 3})

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 6)

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 3)

\frac{1}{3} (2 ln (x + 3) + ln (x) - ln (x^{2} - 1))

lo g_{2} (x) - 5 lo g_{2} (y)

What is simplify-log_{10}(5.4*10^{-4}) ?
The solution to simplify-log_{10}(5.4*10^{-4}) is -log_{10}(5.4)+4