What is simplify-log_{10}(1.2*10^3) ?

The solution to simplify-log_{10}(1.2*10^3) is -log_{10}(1.2)-3

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simplify-log_{10}(1.2*10^3)

simplify

- lo g_{10} (1.2 \cdot 1 0^{3})

- lo g_{10} (1.2) - 3

Decimal Notation

- 3.07918 \dots

Solution steps

- lo g_{10} (1.2 \cdot 1 0^{3})

Apply log rule:

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

lo g_{10} (1.2 \cdot 1 0^{3}) = lo g_{10} (1.2) + lo g_{10} (1 0^{3})

= - (lo g_{10} (1.2) + lo g_{10} (1 0^{3}))

Apply log rule:

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

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

= - (lo g_{10} (1.2) + 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (1.2) + 3)

Distribute parentheses

= - (lo g_{10} (1.2)) - (3)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (1.2) - 3

ln (\frac{x ^{2} - 25}{x ^{4}})

\frac{ln ( a )}{2} - ln (b) - 3 ln (c)

ln (\frac{- 4 i}{1 - i})

ln (\frac{b ^{\frac{1}{2}}}{c ( 0.8 - c )})

ln (x^{3}) + ln (x)

What is simplify-log_{10}(1.2*10^3) ?
The solution to simplify-log_{10}(1.2*10^3) is -log_{10}(1.2)-3