What is simplify-log_{10}(5.011*10^{-5}) ?

The solution to simplify-log_{10}(5.011*10^{-5}) is -log_{10}(5.011)+5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-log_{10}(5.011*10^{-5})

simplify

- lo g_{10} (5.011 \cdot 1 0^{- 5})

- lo g_{10} (5.011) + 5

Decimal Notation

4.30007 \dots

Solution steps

- lo g_{10} (5.011 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (5.011 \cdot 1 0^{- 5}) = lo g_{10} (5.011) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (5.011) + lo g_{10} (1 0^{- 5}))

Apply log rule:

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

lo g_{10} (1 0^{- 5}) = - 5 lo g_{10} (10)

= - (lo g_{10} (5.011) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (5.011) - 5)

Distribute parentheses

= - (lo g_{10} (5.011)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (5.011) + 5

ln (\frac{1}{49})

ln (\frac{x ^{3} x ^{2} + 1}{( x + 1 ) ^{2}})

ln (\frac{20}{30})

What is simplify-log_{10}(5.011*10^{-5}) ?
The solution to simplify-log_{10}(5.011*10^{-5}) is -log_{10}(5.011)+5