What is simplify-log_{10}(1.48*10^{-3}) ?

The solution to simplify-log_{10}(1.48*10^{-3}) is -log_{10}(1.48)+3

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simplify-log_{10}(1.48*10^{-3})

simplify

- lo g_{10} (1.48 \cdot 1 0^{- 3})

- lo g_{10} (1.48) + 3

Decimal Notation

2.82973 \dots

Solution steps

- lo g_{10} (1.48 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (1.48 \cdot 1 0^{- 3}) = lo g_{10} (1.48) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (1.48) + lo g_{10} (1 0^{- 3}))

Apply log rule:

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

lo g_{10} (1 0^{- 3}) = - 3 lo g_{10} (10)

= - (lo g_{10} (1.48) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (1.48) - 3)

Distribute parentheses

= - (lo g_{10} (1.48)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (1.48) + 3

3 ln ∣ x - 1 ∣ - \frac{1}{3} ln ∣ 3 x - 6 ∣ + c

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (- 1 - \frac{1}{4} - \frac{3}{4})

ln (x) - ln (3 x)

ln (\frac{1}{1 - 0.97})

ln (\frac{e ^{8} - 1}{e ^{2} - 1}) - 3

What is simplify-log_{10}(1.48*10^{-3}) ?
The solution to simplify-log_{10}(1.48*10^{-3}) is -log_{10}(1.48)+3