What is simplify-log_{10}(1.94*10^{-7}) ?

The solution to simplify-log_{10}(1.94*10^{-7}) is -log_{10}(1.94)+7

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simplify-log_{10}(1.94*10^{-7})

simplify

- lo g_{10} (1.94 \cdot 1 0^{- 7})

- lo g_{10} (1.94) + 7

Decimal Notation

6.71219 \dots

Solution steps

- lo g_{10} (1.94 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (1.94 \cdot 1 0^{- 7}) = lo g_{10} (1.94) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (1.94) + lo g_{10} (1 0^{- 7}))

Apply log rule:

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

lo g_{10} (1 0^{- 7}) = - 7 lo g_{10} (10)

= - (lo g_{10} (1.94) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (1.94) - 7)

Distribute parentheses

= - (lo g_{10} (1.94)) - (- 7)

Apply minus-plus rules

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

= - lo g_{10} (1.94) + 7

\frac{1}{4} ln (\frac{y}{x} - 1) - \frac{5}{4} ln (\frac{y}{x} + 3) - ln (x)

lo g_{10} (\frac{3}{x ^{2} - y ^{2}})

ln (\frac{x y ^{2}}{e ^{3} z ^{4}})

54 \cdot ln (\frac{75}{54})

\frac{1}{4} ln (\frac{11}{5})

What is simplify-log_{10}(1.94*10^{-7}) ?
The solution to simplify-log_{10}(1.94*10^{-7}) is -log_{10}(1.94)+7