What is simplify-log_{10}(3.16*10^2) ?

The solution to simplify-log_{10}(3.16*10^2) is -log_{10}(3.16)-2

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simplify-log_{10}(3.16*10^2)

simplify

- lo g_{10} (3.16 \cdot 1 0^{2})

- lo g_{10} (3.16) - 2

Decimal Notation

- 2.49968 \dots

Solution steps

- lo g_{10} (3.16 \cdot 1 0^{2})

Apply log rule:

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

lo g_{10} (3.16 \cdot 1 0^{2}) = lo g_{10} (3.16) + lo g_{10} (1 0^{2})

= - (lo g_{10} (3.16) + 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} (3.16) + 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (3.16) + 2)

Distribute parentheses

= - (lo g_{10} (3.16)) - (2)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (3.16) - 2

2 x^{2} + ln (3 x)

- lo g_{10} (1.15 \cdot 1 0^{- 15})

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

lo g_{5} (7 x)

ln (9 x^{3} + 10) - ln (2 x^{2} + 5)

What is simplify-log_{10}(3.16*10^2) ?
The solution to simplify-log_{10}(3.16*10^2) is -log_{10}(3.16)-2