What is simplify-log_{10}(8.7*10^{-9}) ?

The solution to simplify-log_{10}(8.7*10^{-9}) is -log_{10}(8.7)+9

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simplify-log_{10}(8.7*10^{-9})

simplify

- lo g_{10} (8.7 \cdot 1 0^{- 9})

- lo g_{10} (8.7) + 9

Decimal Notation

8.06048 \dots

Solution steps

- lo g_{10} (8.7 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (8.7 \cdot 1 0^{- 9}) = lo g_{10} (8.7) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (8.7) + 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} (8.7) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (8.7) - 9)

Distribute parentheses

= - (lo g_{10} (8.7)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (8.7) + 9

\frac{1}{2} lo g_{10} (x) + lo g_{10} (y)

0.33 \cdot lo g_{10} (0.33) + 0.67 \cdot lo g_{10} (0.67)

ln (x) + ln (x) + 3 ln (3 x)

lo g_{10} (\frac{2}{3})

ln (a - b) + ln (a + b)

What is simplify-log_{10}(8.7*10^{-9}) ?
The solution to simplify-log_{10}(8.7*10^{-9}) is -log_{10}(8.7)+9