What is simplify-log_{10}(3.98*10^{-7}) ?

The solution to simplify-log_{10}(3.98*10^{-7}) is -log_{10}(3.98)+7

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simplify-log_{10}(3.98*10^{-7})

simplify

- lo g_{10} (3.98 \cdot 1 0^{- 7})

- lo g_{10} (3.98) + 7

Decimal Notation

6.40011 \dots

Solution steps

- lo g_{10} (3.98 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (3.98 \cdot 1 0^{- 7}) = lo g_{10} (3.98) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (3.98) + 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} (3.98) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (3.98) - 7)

Distribute parentheses

= - (lo g_{10} (3.98)) - (- 7)

Apply minus-plus rules

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

= - lo g_{10} (3.98) + 7

3.14 + lo g_{10} (\frac{1.875}{0.625})

e ln (ey) - e - ln (y) + 1

ln (\frac{24}{74})

\frac{1}{\frac{1}{3} - 1} \cdot ln (\frac{0.75 - 1}{0.75 \cdot \frac{1}{3} - 1})

ln (x - 1) + 2 ln (x + 4) - 3 ln (x - 5)

What is simplify-log_{10}(3.98*10^{-7}) ?
The solution to simplify-log_{10}(3.98*10^{-7}) is -log_{10}(3.98)+7