What is simplify-log_{10}(1.2*10^{-2}) ?

The solution to simplify-log_{10}(1.2*10^{-2}) is -log_{10}(1.2)+2

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simplify-log_{10}(1.2*10^{-2})

simplify

- lo g_{10} (1.2 \cdot 1 0^{- 2})

- lo g_{10} (1.2) + 2

Decimal Notation

1.92081 \dots

Solution steps

- lo g_{10} (1.2 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (1.2 \cdot 1 0^{- 2}) = lo g_{10} (1.2) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (1.2) + lo g_{10} (1 0^{- 2}))

Apply log rule:

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

lo g_{10} (1 0^{- 2}) = - 2 lo g_{10} (10)

= - (lo g_{10} (1.2) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (1.2) - 2)

Distribute parentheses

= - (lo g_{10} (1.2)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (1.2) + 2

ln (x) + ln (sin (x))

3 ln (10) - lo g_{10} (5) - lo g_{10} (2)

\frac{1}{3} ln (2 + 3)

- 2 ln (\frac{3}{4}) - ln (6)

3 (lo g_{6} (x) + 2 lo g_{6} (y) - 3 lo g_{6} (z))

What is simplify-log_{10}(1.2*10^{-2}) ?
The solution to simplify-log_{10}(1.2*10^{-2}) is -log_{10}(1.2)+2