What is simplify-log_{10}(1.7(10^{-9})) ?

The solution to simplify-log_{10}(1.7(10^{-9})) is -log_{10}(1.7)+9

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simplify-log_{10}(1.7(10^{-9}))

simplify

- lo g_{10} (1.7 (1 0^{- 9}))

- lo g_{10} (1.7) + 9

Decimal Notation

8.76955 \dots

Solution steps

- lo g_{10} (1.7 (1 0^{- 9}))

Apply log rule:

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

lo g_{10} (1.7 (1 0^{- 9})) = lo g_{10} (1.7) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (1.7) + 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} (1.7) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (1.7) - 9)

Distribute parentheses

= - (lo g_{10} (1.7)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (1.7) + 9

182000 (ln (0.44) - ln (1.3))

3.74 + lo g_{10} (\frac{0.0005}{0.0495})

- ln (t + 60) + ln (60)

- ln ∣ x ∣ + 5 ln ∣ x - 1 ∣

ln (\infty) - ln (- \infty)

What is simplify-log_{10}(1.7(10^{-9})) ?
The solution to simplify-log_{10}(1.7(10^{-9})) is -log_{10}(1.7)+9