What is simplify-log_{10}(1.33\times 10^{-3}) ?

The solution to simplify-log_{10}(1.33\times 10^{-3}) is -log_{10}(1.33)+3

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simplify-log_{10}(1.33\times 10^{-3})

simplify

- lo g_{10} (1.33 \cdot 1 0^{- 3})

- lo g_{10} (1.33) + 3

Decimal Notation

2.87614 \dots

Solution steps

- lo g_{10} (1.33 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (1.33 \cdot 1 0^{- 3}) = lo g_{10} (1.33) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (1.33) + 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} (1.33) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (1.33) - 3)

Distribute parentheses

= - (lo g_{10} (1.33)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (1.33) + 3

lo g_{2} (\frac{x y}{z t})

2 ln (x) + 2 ln (x + 2)

lo g_{6} (30) + lo g_{6} (5)

lo g_{2} (5 ab)

lo g_{7} (\frac{x + 8}{5 x - 10})

What is simplify-log_{10}(1.33\times 10^{-3}) ?
The solution to simplify-log_{10}(1.33\times 10^{-3}) is -log_{10}(1.33)+3