What is simplify-log_{10}(6.2*10^{-10}) ?

The solution to simplify-log_{10}(6.2*10^{-10}) is -log_{10}(6.2)+10

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simplify-log_{10}(6.2*10^{-10})

simplify

- lo g_{10} (6.2 \cdot 1 0^{- 10})

- lo g_{10} (6.2) + 10

Decimal Notation

9.20760 \dots

Solution steps

- lo g_{10} (6.2 \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (6.2 \cdot 1 0^{- 10}) = lo g_{10} (6.2) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (6.2) + lo g_{10} (1 0^{- 10}))

Apply log rule:

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

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

= - (lo g_{10} (6.2) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (6.2) - 10)

Distribute parentheses

= - (lo g_{10} (6.2)) - (- 10)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (6.2) + 10

lo g_{4} (x^{5}) - lo g_{4} (x^{3})

3 ln (x) - \frac{2}{3} ln (x + 1) + ln (y) - 3 ln (z)

3 lo g_{7} (2 x) - 2 lo g_{7} (3 y)

\frac{1}{2} lo g_{2} (6) - 2 lo g_{2} (5)

\frac{1}{2} lo g_{2} (6) - 2 lo g_{2} (7)

What is simplify-log_{10}(6.2*10^{-10}) ?
The solution to simplify-log_{10}(6.2*10^{-10}) is -log_{10}(6.2)+10