What is the answer to 5+ln(x)=(14)/(ln(x)) ?

The answer to 5+ln(x)=(14)/(ln(x)) is x=e^2,x= 1/(e^7)

Solve for x: 5+ln(x)=(14)/(ln(x))

The solution is x=e^2,x= 1/(e^7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5 + ln (x) = \frac{14}{ln ( x )}

x = e^{2}, x = \frac{1}{e ^{7}}

Solution steps

5 + ln (x) = \frac{14}{ln ( x )}

Multiply both sides by

ln (x)

5 ln (x) + ln (x) ln (x) = \frac{14}{ln ( x )} ln (x)

Simplify

5 ln (x) + ln (x) ln (x) : 5 ln (x) + ln^{2} (x)

5 ln (x) + ln^{2} (x) = 14

Rewrite the equation with

ln (x) = u

5 u + u^{2} = 14

Solve

5 u + u^{2} = 14 : u = 2, u = - 7

u = 2, u = - 7

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 2 : x = e^{2}

Solve

ln (x) = - 7 : x = \frac{1}{e ^{7}}

x = e^{2}, x = \frac{1}{e ^{7}}

Verify Solutions:

x = e^{2}

True

, x = \frac{1}{e ^{7}}

True

The solutions are

x = e^{2}, x = \frac{1}{e ^{7}}

ln (x - 4) + ln (x + 3) = ln (x - 13)

lo g_{2} (t) = 6

x, ln (y) = x + ln (x)

2 lo g_{x} (3) + lo g_{x} (9) = 4

ln (x + 11) + ln (x - 4) = 2 ln (x)

What is the answer to 5+ln(x)=(14)/(ln(x)) ?
The answer to 5+ln(x)=(14)/(ln(x)) is x=e^2,x= 1/(e^7)
Solve for x: 5+ln(x)=(14)/(ln(x))
The solution is x=e^2,x= 1/(e^7)