What is simplify-log_{10}(7.9*10^{-9}) ?

The solution to simplify-log_{10}(7.9*10^{-9}) is -log_{10}(7.9)+9

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simplify-log_{10}(7.9*10^{-9})

simplify

- lo g_{10} (7.9 \cdot 1 0^{- 9})

- lo g_{10} (7.9) + 9

Decimal Notation

8.10237 \dots

Solution steps

- lo g_{10} (7.9 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (7.9 \cdot 1 0^{- 9}) = lo g_{10} (7.9) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (7.9) + lo g_{10} (1 0^{- 9}))

Apply log rule:

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

lo g_{10} (1 0^{- 9}) = - 9 lo g_{10} (10)

= - (lo g_{10} (7.9) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (7.9) - 9)

Distribute parentheses

= - (lo g_{10} (7.9)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (7.9) + 9

lo g_{2} (x y) - \frac{1}{3} lo g_{2} (x^{2})

f (x) = ln (\frac{3 ^{x} 6 ^{3 x}}{2 ^{3 x}})

\frac{1}{2} lo g_{10} (x) - lo g_{10} (2) - 7 lo g_{10} (m)

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

lo g_{10} (2 x + 9) - lo g_{10} (x)

What is simplify-log_{10}(7.9*10^{-9}) ?
The solution to simplify-log_{10}(7.9*10^{-9}) is -log_{10}(7.9)+9