What is log_{10}(40)-log_{10}(2.5) ?

The solution to log_{10}(40)-log_{10}(2.5) is 4log_{10}(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(40)-log_{10}(2.5)

simplify

lo g_{10} (40) - lo g_{10} (2.5)

4 lo g_{10} (2)

Decimal Notation

1.20411 \dots

Solution steps

lo g_{10} (40) - lo g_{10} (2.5)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (40) - lo g_{10} (2.5) = lo g_{10} (\frac{40}{2.5})

= lo g_{10} (\frac{40}{2.5})

Divide the numbers:

\frac{40}{2.5} = 16

= lo g_{10} (16)

Factor the number:

16 = 2^{4}

= lo g_{10} (2^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (2^{4}) = 4 lo g_{10} (2)

= 4 lo g_{10} (2)

ln (\frac{- 1}{x})

ln (\frac{x + 3}{4 y})

- lo g_{10} (1.12 \cdot 1 0^{- 4})

lo g_{5} (x^{4} y^{3})

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

What is log_{10}(40)-log_{10}(2.5) ?
The solution to log_{10}(40)-log_{10}(2.5) is 4log_{10}(2)