What is simplify-log_{10}(2.8*10^{-3}) ?

The solution to simplify-log_{10}(2.8*10^{-3}) is -log_{10}(2.8)+3

Popular >

simplify-log_{10}(2.8*10^{-3})

simplify

- lo g_{10} (2.8 \cdot 1 0^{- 3})

- lo g_{10} (2.8) + 3

Decimal Notation

2.55284 \dots

Solution steps

- lo g_{10} (2.8 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (2.8 \cdot 1 0^{- 3}) = lo g_{10} (2.8) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (2.8) + 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} (2.8) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (2.8) - 3)

Distribute parentheses

= - (lo g_{10} (2.8)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (2.8) + 3

lo g_{10} (x^{3}) - lo g_{10} (x^{2})

lo g_{e} (\frac{17}{4})

5 lo g_{b} (x) - lo g_{b} (y) + \frac{1}{4} lo g_{b} (z)

lo g_{2} (6) - \frac{1}{2} lo g_{2} (3)

5 ln (x^{3}) - \frac{1}{3} ln (7 - x^{3})

What is simplify-log_{10}(2.8*10^{-3}) ?
The solution to simplify-log_{10}(2.8*10^{-3}) is -log_{10}(2.8)+3