What is simplify-log_{10}(1.33*10^{-12}) ?

The solution to simplify-log_{10}(1.33*10^{-12}) is -log_{10}(1.33)+12

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simplify-log_{10}(1.33*10^{-12})

simplify

- lo g_{10} (1.33 \cdot 1 0^{- 12})

- lo g_{10} (1.33) + 12

Decimal Notation

11.87614 \dots

Solution steps

- lo g_{10} (1.33 \cdot 1 0^{- 12})

Apply log rule:

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

lo g_{10} (1.33 \cdot 1 0^{- 12}) = lo g_{10} (1.33) + lo g_{10} (1 0^{- 12})

= - (lo g_{10} (1.33) + lo g_{10} (1 0^{- 12}))

Apply log rule:

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

lo g_{10} (1 0^{- 12}) = - 12 lo g_{10} (10)

= - (lo g_{10} (1.33) - 12 lo g_{10} (10))

12 lo g_{10} (10) = 12

= - (lo g_{10} (1.33) - 12)

Distribute parentheses

= - (lo g_{10} (1.33)) - (- 12)

Apply minus-plus rules

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

= - lo g_{10} (1.33) + 12

5 ln (x + 1) + 2 ln (x^{3}) - ln (x)

0.5 lo g_{10} (c) + 5 lo g_{10} (d)

lo g_{2} (\frac{1}{12}) + 3.4387

2 ln (2 x) - 3 ln (3 x)

- x (ln (5) - ln (3))

What is simplify-log_{10}(1.33*10^{-12}) ?
The solution to simplify-log_{10}(1.33*10^{-12}) is -log_{10}(1.33)+12