What is simplify-log_{3}(75*10^{-3}) ?

The solution to simplify-log_{3}(75*10^{-3}) is -log_{3}(75)+3log_{3}(10)

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simplify-log_{3}(75*10^{-3})

simplify

- lo g_{3} (75 \cdot 1 0^{- 3})

- lo g_{3} (75) + 3 lo g_{3} (10)

Decimal Notation

2.35776 \dots

Solution steps

- lo g_{3} (75 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{3} (75 \cdot 1 0^{- 3}) = lo g_{3} (75) + lo g_{3} (1 0^{- 3})

= - (lo g_{3} (75) + lo g_{3} (1 0^{- 3}))

Apply log rule:

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

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

= - (lo g_{3} (75) - 3 lo g_{3} (10))

Distribute parentheses

= - (lo g_{3} (75)) - (- 3 lo g_{3} (10))

Apply minus-plus rules

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

= - lo g_{3} (75) + 3 lo g_{3} (10)

ln (\frac{28.5}{43.5})

\frac{1}{2} ln (4 x) - \frac{1}{2} ln (x^{2})

12 ln (x + 0.125) + 13 ln (4 x + 1)

2 lo g_{2} (2 x + 5) + 6 lo g_{2} (6 x + 1)

(ln (7) - ln (5)) \cdot 50

What is simplify-log_{3}(75*10^{-3}) ?
The solution to simplify-log_{3}(75*10^{-3}) is -log_{3}(75)+3log_{3}(10)