What is simplify-log_{10}(5.2*10^{-6}) ?

The solution to simplify-log_{10}(5.2*10^{-6}) is -log_{10}(5.2)+6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-log_{10}(5.2*10^{-6})

simplify

- lo g_{10} (5.2 \cdot 1 0^{- 6})

- lo g_{10} (5.2) + 6

Decimal Notation

5.28399 \dots

Solution steps

- lo g_{10} (5.2 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (5.2 \cdot 1 0^{- 6}) = lo g_{10} (5.2) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (5.2) + lo g_{10} (1 0^{- 6}))

Apply log rule:

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

lo g_{10} (1 0^{- 6}) = - 6 lo g_{10} (10)

= - (lo g_{10} (5.2) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (5.2) - 6)

Distribute parentheses

= - (lo g_{10} (5.2)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (5.2) + 6

ln (29) - ln (2)

ln (12) + ln (27)

ln (\frac{e ^{a}}{b})

ln (C e^{5.4444})

4 ln (3) + 5 ln (2)

What is simplify-log_{10}(5.2*10^{-6}) ?
The solution to simplify-log_{10}(5.2*10^{-6}) is -log_{10}(5.2)+6