What is simplify-log_{10}(3.55*10^{-32}) ?

The solution to simplify-log_{10}(3.55*10^{-32}) is -log_{10}(3.55)+32

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simplify-log_{10}(3.55*10^{-32})

simplify

- lo g_{10} (3.55 \cdot 1 0^{- 32})

- lo g_{10} (3.55) + 32

Decimal Notation

31.44977 \dots

Solution steps

- lo g_{10} (3.55 \cdot 1 0^{- 32})

Apply log rule:

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

lo g_{10} (3.55 \cdot 1 0^{- 32}) = lo g_{10} (3.55) + lo g_{10} (1 0^{- 32})

= - (lo g_{10} (3.55) + lo g_{10} (1 0^{- 32}))

Apply log rule:

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

lo g_{10} (1 0^{- 32}) = - 32 lo g_{10} (10)

= - (lo g_{10} (3.55) - 32 lo g_{10} (10))

32 lo g_{10} (10) = 32

= - (lo g_{10} (3.55) - 32)

Distribute parentheses

= - (lo g_{10} (3.55)) - (- 32)

Apply minus-plus rules

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

= - lo g_{10} (3.55) + 32

(ln (b + 2 a) - ln (a)) k - (a + 2 b) (a + b)

8 ln (x + 6) - 5 ln (x)

- lo g_{10} (2.17 \cdot 1 0^{- 6})

5 ln (x) + ln (x^{2} + 7) - 9 ln (x + 7)

lo g_{10} (3.436 + 1) - lo g_{10} (1.718)

What is simplify-log_{10}(3.55*10^{-32}) ?
The solution to simplify-log_{10}(3.55*10^{-32}) is -log_{10}(3.55)+32