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

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

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

simplify

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

- lo g_{10} (5) - 5

Decimal Notation

- 5.69897 \dots

Solution steps

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

Apply log rule:

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

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

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

5 lo g_{10} (10) = 5

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

\frac{1}{2} \cdot ln (\frac{x + 1}{x - 1})

ln (\frac{10}{10000000})

lo g_{3} (2) + lo g_{3} (5) - lo g_{3} (4)

∣ 5 x + 2 ∣ - ∣ x^{2} + 2 ∣ + ln (4 x)

2 ln (x + 1) - ln (x)

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