What is simplify-log_{10}(1.1*10^{-2}) ?

The solution to simplify-log_{10}(1.1*10^{-2}) is -log_{10}(1.1)+2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-log_{10}(1.1*10^{-2})

simplify

- lo g_{10} (1.1 \cdot 1 0^{- 2})

- lo g_{10} (1.1) + 2

Decimal Notation

1.95860 \dots

Solution steps

- lo g_{10} (1.1 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (1.1 \cdot 1 0^{- 2}) = lo g_{10} (1.1) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (1.1) + lo g_{10} (1 0^{- 2}))

Apply log rule:

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

lo g_{10} (1 0^{- 2}) = - 2 lo g_{10} (10)

= - (lo g_{10} (1.1) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (1.1) - 2)

Distribute parentheses

= - (lo g_{10} (1.1)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (1.1) + 2

lo g_{e} (\frac{e}{2})

ln (\frac{6 x 1 + 4 x}{( x - 5 ) ^{11}})

- 2 ln (x) - 3 ln (y) + ln (a) + 4 ln (b)

ln (4 b)

What is simplify-log_{10}(1.1*10^{-2}) ?
The solution to simplify-log_{10}(1.1*10^{-2}) is -log_{10}(1.1)+2