What is (4pi*10^{-7}*100^2)/(4pi)ln(1/7) ?

The solution to (4pi*10^{-7}*100^2)/(4pi)ln(1/7) is -1/1000 ln(7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (4pi10^{-7}100^2)/(4pi)ln(1/7)

Solution

simplify

\frac{4 π \cdot 1 0 ^{- 7} \cdot 10 0 ^{2}}{4 π} ln (\frac{1}{7})

Solution

- \frac{1}{1000} ln (7)

Decimal Notation

- 0.00194 \dots

Solution steps

\frac{4 π 1 0 ^{- 7} \cdot 10 0 ^{2}}{4 π} ln (\frac{1}{7})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{7}) = ln (1) - ln (7)

= \frac{1 0 ^{- 7} \cdot 10 0 ^{2} \cdot 4 π}{4 π} (ln (1) - ln (7))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 π 1 0 ^{- 7} \cdot 10 0 ^{2} ( ln ( 1 ) - ln ( 7 ) )}{4 π}

Cancel the common factor:

4

= \frac{π 1 0 ^{- 7} \cdot 10 0 ^{2} ( ln ( 1 ) - ln ( 7 ) )}{π}

Cancel the common factor:

π

= 1 0^{- 7} \cdot 10 0^{2} (ln (1) - ln (7))

Factor integer

10 = 2 \cdot 5

= (2 \cdot 5)^{- 7} \cdot 10 0^{2} (ln (1) - ln (7))

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{- 7} = 2^{- 7} \cdot 5^{- 7}

= 2^{- 7} \cdot 5^{- 7} \cdot 10 0^{2} (ln (1) - ln (7))

Factor integer

100 = 2^{2} \cdot 5^{2}

= 2^{- 7} \cdot 5^{- 7} (2^{2} \cdot 5^{2})^{2} (ln (1) - ln (7))

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2^{2} \cdot 5^{2})^{2} = (2^{2})^{2} (5^{2})^{2}

= 2^{- 7} \cdot 5^{- 7} (2^{2})^{2} (5^{2})^{2} (ln (1) - ln (7))

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(2^{2})^{2} = 2^{2 \cdot 2}, (5^{2})^{2} = 5^{2 \cdot 2}

= 2^{- 7} \cdot 5^{- 7} \cdot 2^{2 \cdot 2} \cdot 5^{2 \cdot 2} (ln (1) - ln (7))

Refine

= 2^{- 7} \cdot 5^{- 7} \cdot 2^{4} \cdot 5^{4} (ln (1) - ln (7))

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{- 7} \cdot 2^{4} = 2^{- 7 + 4}

= 5^{- 7} \cdot 2^{- 7 + 4} \cdot 5^{4} (ln (1) - ln (7))

Add/Subtract the numbers:

- 7 + 4 = - 3

= 5^{- 7} \cdot 2^{- 3} \cdot 5^{4} (ln (1) - ln (7))

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

5^{- 7} \cdot 5^{4} = 5^{- 7 + 4}

= 2^{- 3} \cdot 5^{- 7 + 4} (ln (1) - ln (7))

Add/Subtract the numbers:

- 7 + 4 = - 3

= 2^{- 3} \cdot 5^{- 3} (ln (1) - ln (7))

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

2^{- 3} = \frac{1}{2 ^{3}}

= 5^{- 3} \cdot \frac{1}{2 ^{3}} (ln (1) - ln (7))

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

5^{- 3} = \frac{1}{5 ^{3}}

= \frac{1}{2 ^{3}} \cdot \frac{1}{5 ^{3}} (ln (1) - ln (7))

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 ^{3} \cdot 5 ^{3}} (ln (1) - ln (7))

\frac{1 \cdot 1}{2 ^{3} \cdot 5 ^{3}} = \frac{1}{1000}

= \frac{1}{1000} (ln (1) - ln (7))

Apply log rule:

lo g_{a} (1) = 0

= \frac{1}{1000} (- ln (7) + 0)

0 - ln (7) = - ln (7)

= \frac{1}{1000} (- ln (7))

Remove parentheses:

(- a) = - a

= - ln (7) \frac{1}{1000}

Popular Examples

simplify ln(b/x)-ln(a/x)simplify

ln (\frac{b}{x}) - ln (\frac{a}{x})

simplify ln((a^{-2})/(b^4c^{-3)})simplify

ln (\frac{a ^{- 2}}{b ^{4} c ^{- 3}})

simplify ln(y/2*e^{-y|x|})simplify

ln (\frac{y}{2} \cdot e^{- y ∣ x ∣})

simplify ln|1+e^{8In}|-ln(3)simplify

ln 1 + e^{8 I n} - ln (3)

simplify ln((0.015)/(0.025))simplify

ln (\frac{0.015}{0.025})

Frequently Asked Questions (FAQ)

What is (4pi*10^{-7}*100^2)/(4pi)ln(1/7) ?
The solution to (4pi*10^{-7}*100^2)/(4pi)ln(1/7) is -1/1000 ln(7)

simplify (4pi*10^{-7}*100^2)/(4pi)ln(1/7)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is (4pi*10^{-7}*100^2)/(4pi)ln(1/7) ?

simplify (4pi10^{-7}100^2)/(4pi)ln(1/7)

What is (4pi10^{-7}100^2)/(4pi)ln(1/7) ?