What is simplify-log_{10}(3*10^6) ?

The solution to simplify-log_{10}(3*10^6) is -log_{10}(3)-6

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simplify-log_{10}(3*10^6)

simplify

- lo g_{10} (3 \cdot 1 0^{6})

- lo g_{10} (3) - 6

Decimal Notation

- 6.47712 \dots

Solution steps

- lo g_{10} (3 \cdot 1 0^{6})

Apply log rule:

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

lo g_{10} (3 \cdot 1 0^{6}) = lo g_{10} (3) + lo g_{10} (1 0^{6})

= - (lo g_{10} (3) + lo g_{10} (1 0^{6}))

Apply log rule:

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

lo g_{10} (1 0^{6}) = 6 lo g_{10} (10)

= - (lo g_{10} (3) + 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (3) + 6)

Distribute parentheses

= - (lo g_{10} (3)) - (6)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (3) - 6

4.74 + lo g_{10} (\frac{0.6}{0.25})

ln (0. 1^{2} \cdot 0. 5^{2} \cdot 1^{2} \cdot 4 \cdot 16)

ln (\frac{85}{75})

ln (\frac{x ^{2} + 2 x - 24}{x})

4 lo g_{9} (u) + 24 lo g_{9} (v) + 4 lo g_{9} (w)

What is simplify-log_{10}(3*10^6) ?
The solution to simplify-log_{10}(3*10^6) is -log_{10}(3)-6