What is simplify-log_{10}(4.8*10^{-6}) ?

The solution to simplify-log_{10}(4.8*10^{-6}) is -log_{10}(4.8)+6

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simplify-log_{10}(4.8*10^{-6})

simplify

- lo g_{10} (4.8 \cdot 1 0^{- 6})

- lo g_{10} (4.8) + 6

Decimal Notation

5.31875 \dots

Solution steps

- lo g_{10} (4.8 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (4.8 \cdot 1 0^{- 6}) = lo g_{10} (4.8) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (4.8) + 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} (4.8) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (4.8) - 6)

Distribute parentheses

= - (lo g_{10} (4.8)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (4.8) + 6

\frac{9}{14} lo g_{10} (\frac{9}{14}) + \frac{5}{14} lo g_{\frac{5}{14}} (x)

ln (\frac{16}{3})

ln (\frac{300}{250})

\frac{1}{t ^{2}} + ln^{2} (t) + 2 ln (t) + 2

lo g_{4} (\frac{1}{64})

What is simplify-log_{10}(4.8*10^{-6}) ?
The solution to simplify-log_{10}(4.8*10^{-6}) is -log_{10}(4.8)+6