What is simplify-log_{10}(6.5*10^{-12}) ?

The solution to simplify-log_{10}(6.5*10^{-12}) is -log_{10}(6.5)+12

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simplify-log_{10}(6.5*10^{-12})

simplify

- lo g_{10} (6.5 \cdot 1 0^{- 12})

- lo g_{10} (6.5) + 12

Decimal Notation

11.18708 \dots

Solution steps

- lo g_{10} (6.5 \cdot 1 0^{- 12})

Apply log rule:

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

lo g_{10} (6.5 \cdot 1 0^{- 12}) = lo g_{10} (6.5) + lo g_{10} (1 0^{- 12})

= - (lo g_{10} (6.5) + lo g_{10} (1 0^{- 12}))

Apply log rule:

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

lo g_{10} (1 0^{- 12}) = - 12 lo g_{10} (10)

= - (lo g_{10} (6.5) - 12 lo g_{10} (10))

12 lo g_{10} (10) = 12

= - (lo g_{10} (6.5) - 12)

Distribute parentheses

= - (lo g_{10} (6.5)) - (- 12)

Apply minus-plus rules

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

= - lo g_{10} (6.5) + 12

4 lo g_{b} (v) + 3 lo g_{b} (q)

ln (\frac{6}{3.1 4 ^{2}})

ln ∣ z + 4 ∣ + 6 (\frac{1}{5} ln ∣ z - 1 ∣ - \frac{1}{5} ln ∣ z + 4 ∣) + ln ∣ x ∣

\frac{ln ( u ^{2} ) - ln ( u ) + ln ( u )}{ln ( u ^{3} )}

ln (\frac{x ^{4} + 1 - x ^{2}}{x ^{4} + 1 + x ^{2}})

What is simplify-log_{10}(6.5*10^{-12}) ?
The solution to simplify-log_{10}(6.5*10^{-12}) is -log_{10}(6.5)+12