en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-log_{10}(0.25)

Solution

simplify

- lo g_{10} (0.25)

Solution

2 lo g_{10} (2)

+1

Decimal Notation

0.60205 \dots

Solution steps

- lo g_{10} (0.25)

0.25 = \frac{25}{100}

= - lo g_{10} (\frac{25}{100})

Cancel the numbers:

\frac{25}{100} = \frac{1}{4}

= - lo g_{10} (\frac{1}{4})

\frac{1}{4} = 4^{- 1}

= - lo g_{10} (4^{- 1})

Apply log rule:

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

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

= - (- 1 \cdot lo g_{10} (4))

Apply rule:

1 \cdot a = a

- 1 \cdot lo g_{10} (4) = - lo g_{10} (4)

= - (- lo g_{10} (4))

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

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

Apply rule:

- (- a) = a

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

= 2 lo g_{10} (2)

Popular Examples

expand (x-2)(x+4)(x+6)expand

(x - 2) (x + 4) (x + 6)

simplify sqrt(n^3)simplify

n^{3}

expand (X+3)^2 expand

(X + 3)^{2}

simplify (x^2-3x-10)/(x-5)simplify

\frac{x ^{2} - 3 x - 10}{x - 5}

factor 6ab+4a-15b-10 factor

6 ab + 4 a - 15 b - 10

Frequently Asked Questions (FAQ)

What is simplify-log_{10}(0.25) ?
The solution to simplify-log_{10}(0.25) is 2log_{10}(2)