What is simplify-log_{10}(3646974099x10^{-3}) ?

The solution to simplify-log_{10}(3646974099x10^{-3}) is -log_{10}(3646974099)-log_{10}(x)+3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-log_{10}(3646974099x10^{-3})

simplify

- lo g_{10} (3646974099 x 1 0^{- 3})

- lo g_{10} (3646974099) - lo g_{10} (x) + 3

Solution steps

- lo g_{10} (3646974099 x \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (3646974099 x \cdot 1 0^{- 3}) = lo g_{10} (3646974099) + lo g_{10} (x) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (x) + lo g_{10} (1 0^{- 3}) + lo g_{10} (3646974099))

Apply log rule:

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

lo g_{10} (1 0^{- 3}) = - 3 lo g_{10} (10)

= - (lo g_{10} (3646974099) + lo g_{10} (x) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (x) + lo g_{10} (3646974099) - 3)

Distribute parentheses

= - (lo g_{10} (3646974099)) - (lo g_{10} (x)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (3646974099) - lo g_{10} (x) + 3

ln (20 x^{3}) - ln (2 x^{0})

ln (4 x + 5) + ln (6 x)

ln (- 9 e^{- t})

- ln (x^{5} y^{5})

- lo g_{10} (3.33 \cdot 1 0^{- 12})

What is simplify-log_{10}(3646974099x10^{-3}) ?
The solution to simplify-log_{10}(3646974099x10^{-3}) is -log_{10}(3646974099)-log_{10}(x)+3