What is simplify-log_{10}(3*10^5) ?

The solution to simplify-log_{10}(3*10^5) is -log_{10}(3)-5

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simplify-log_{10}(3*10^5)

simplify

- lo g_{10} (3 \cdot 1 0^{5})

- lo g_{10} (3) - 5

Decimal Notation

- 5.47712 \dots

Solution steps

- lo g_{10} (3 \cdot 1 0^{5})

Apply log rule:

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

lo g_{10} (3 \cdot 1 0^{5}) = lo g_{10} (3) + lo g_{10} (1 0^{5})

= - (lo g_{10} (3) + lo g_{10} (1 0^{5}))

Apply log rule:

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

lo g_{10} (1 0^{5}) = 5 lo g_{10} (10)

= - (lo g_{10} (3) + 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (3) + 5)

Distribute parentheses

= - (lo g_{10} (3)) - (5)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (3) - 5

3 ln (\frac{y}{x} - 1)

\frac{1}{2} (ln (11) - 3 ln (2))

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

6 lo g_{4} (c) + 5 lo g_{4} (a)

ln (92)

What is simplify-log_{10}(3*10^5) ?
The solution to simplify-log_{10}(3*10^5) is -log_{10}(3)-5