What is simplify-log_{10}(3.5*10^{11}) ?

The solution to simplify-log_{10}(3.5*10^{11}) is -log_{10}(3.5)-11

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simplify-log_{10}(3.5*10^{11})

simplify

- lo g_{10} (3.5 \cdot 1 0^{11})

- lo g_{10} (3.5) - 11

Decimal Notation

- 11.54406 \dots

Solution steps

- lo g_{10} (3.5 \cdot 1 0^{11})

Apply log rule:

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

lo g_{10} (3.5 \cdot 1 0^{11}) = lo g_{10} (3.5) + lo g_{10} (1 0^{11})

= - (lo g_{10} (3.5) + lo g_{10} (1 0^{11}))

Apply log rule:

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

lo g_{10} (1 0^{11}) = 11 lo g_{10} (10)

= - (lo g_{10} (3.5) + 11 lo g_{10} (10))

11 lo g_{10} (10) = 11

= - (lo g_{10} (3.5) + 11)

Distribute parentheses

= - (lo g_{10} (3.5)) - (11)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (3.5) - 11

ln (k e^{- bk} b^{2})

\frac{1}{2} ln b^{2} + 1 - \frac{1}{2} ln a^{2} + 1

lo g_{1.8} (\frac{5.07}{3.92}) + 51.7 - 51.6

ln (2 \cdot 1 0^{6})

ln (2) + 8 ln (x)

What is simplify-log_{10}(3.5*10^{11}) ?
The solution to simplify-log_{10}(3.5*10^{11}) is -log_{10}(3.5)-11