What is simplify-log_{10}(2.6*10^{-4}) ?

The solution to simplify-log_{10}(2.6*10^{-4}) is -log_{10}(2.6)+4

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simplify-log_{10}(2.6*10^{-4})

simplify

- lo g_{10} (2.6 \cdot 1 0^{- 4})

- lo g_{10} (2.6) + 4

Decimal Notation

3.58502 \dots

Solution steps

- lo g_{10} (2.6 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (2.6 \cdot 1 0^{- 4}) = lo g_{10} (2.6) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (2.6) + 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} (2.6) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (2.6) - 4)

Distribute parentheses

= - (lo g_{10} (2.6)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (2.6) + 4

lo g_{x} (\frac{1}{16})

3 ln (x) - 4 ln (y) - 5 ln (z)

- lo g_{10} (5 \times 1 0^{- 5})

5 lo g_{b} (x) + 3 lo g_{b} (z)

- 0.45 lo g_{2} (0.45) - 0.55 lo g_{2} (0.55)

What is simplify-log_{10}(2.6*10^{-4}) ?
The solution to simplify-log_{10}(2.6*10^{-4}) is -log_{10}(2.6)+4