en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(1/(sqrt(e^7)))

Solution

simplify

ln (\frac{1}{e ^{7}})

Solution

- \frac{7}{2}

+1

Decimal Notation

- 3.5

Solution steps

ln (\frac{1}{e ^{7}})

\frac{1}{e ^{7}} = \frac{1}{e ^{3} e}

= ln (\frac{1}{e ^{3} e})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (e^{3} e)

Apply log rule:

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

ln (e^{3} e) = ln (e) + ln (e^{3})

= - (ln (e^{3}) + ln (e))

Simplify

ln (e^{3}) : 3

Rewrite as

= - (ln (e^{\frac{1}{2}}) + 3)

Apply log rule

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

assuming

x \geq 0

= - (\frac{1}{2} ln (e) + 3)

Apply log rule:

lo g_{a} (a) = 1

= - (\frac{1}{2} + 3)

Join

\frac{1}{2} + 3 : \frac{7}{2}

= - \frac{7}{2}

Popular Examples

simplify 2sqrt(-3)+3sqrt(-36)-5sqrt(-4)simplify

2 - 3 + 3 - 36 - 5 - 4

expand (x^3+2)^2 expand

(x^{3} + 2)^{2}

simplify (xy)^5 simplify

(x y)^{5}

factor 3+11a+10a^2 factor

3 + 11 a + 10 a^{2}

factor x^3-6x factor

x^{3} - 6 x

Frequently Asked Questions (FAQ)

What is ln(1/(sqrt(e^7))) ?
The solution to ln(1/(sqrt(e^7))) is -7/2