What is simplify-log_{10}(2.92*10^{-14}) ?

The solution to simplify-log_{10}(2.92*10^{-14}) is -log_{10}(2.92)+14

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simplify-log_{10}(2.92*10^{-14})

simplify

- lo g_{10} (2.92 \cdot 1 0^{- 14})

- lo g_{10} (2.92) + 14

Decimal Notation

13.53461 \dots

Solution steps

- lo g_{10} (2.92 \cdot 1 0^{- 14})

Apply log rule:

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

lo g_{10} (2.92 \cdot 1 0^{- 14}) = lo g_{10} (2.92) + lo g_{10} (1 0^{- 14})

= - (lo g_{10} (2.92) + lo g_{10} (1 0^{- 14}))

Apply log rule:

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

lo g_{10} (1 0^{- 14}) = - 14 lo g_{10} (10)

= - (lo g_{10} (2.92) - 14 lo g_{10} (10))

14 lo g_{10} (10) = 14

= - (lo g_{10} (2.92) - 14)

Distribute parentheses

= - (lo g_{10} (2.92)) - (- 14)

Apply minus-plus rules

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

= - lo g_{10} (2.92) + 14

\frac{3}{2} ln ∣ (- 0.5 - 1) ∣ - \frac{3}{2} ln ∣ (- 1 - 1) ∣

ln (x^{3} \cdot (x + 2))

\frac{2 cos ( 2 ln ( x ) )}{x ^{2}} + x^{3}

2 ln (a) - \frac{1}{2} ln (b)

5.8 + lo g_{10} (\frac{0.015}{0.4})

What is simplify-log_{10}(2.92*10^{-14}) ?
The solution to simplify-log_{10}(2.92*10^{-14}) is -log_{10}(2.92)+14