What is simplify-log_{10}(2.1*10^{-7}) ?

The solution to simplify-log_{10}(2.1*10^{-7}) is -log_{10}(2.1)+7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-log_{10}(2.1*10^{-7})

simplify

- lo g_{10} (2.1 \cdot 1 0^{- 7})

- lo g_{10} (2.1) + 7

Decimal Notation

6.67778 \dots

Solution steps

- lo g_{10} (2.1 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (2.1 \cdot 1 0^{- 7}) = lo g_{10} (2.1) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (2.1) + 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} (2.1) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (2.1) - 7)

Distribute parentheses

= - (lo g_{10} (2.1)) - (- 7)

Apply minus-plus rules

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

= - lo g_{10} (2.1) + 7

ln (\frac{0.01 - 2}{0.01})

5 ln (\frac{106}{5})

8 ln (3) - 8 ln (2)

lo g_{e} (\frac{9}{4})

- lo g_{10} (8.07 \cdot 1 0^{- 7})

What is simplify-log_{10}(2.1*10^{-7}) ?
The solution to simplify-log_{10}(2.1*10^{-7}) is -log_{10}(2.1)+7