What is the answer to log_{3}(x)+3log_{x}(3)=4 ?

The answer to log_{3}(x)+3log_{x}(3)=4 is x=27,x=3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{3}(x)+3log_{x}(3)=4

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

x = 27, x = 3

Solution steps

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

Apply log rules

lo g_{3} (x) + \frac{3}{lo g _{3} ( x )} = 4

Rewrite the equation with

lo g_{3} (x) = u

u + \frac{3}{u} = 4

Solve

u + \frac{3}{u} = 4 : u = 3, u = 1

u = 3, u = 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 3 : x = 27

Solve

lo g_{3} (x) = 1 : x = 3

x = 27, x = 3

Verify Solutions:

x = 27

True

, x = 3

True

The solutions are

x = 27, x = 3

- lo g_{10} (x) = 9.44

10 lo g_{10} (x) = 4

10 lo g_{10} (x) = 0

4 - 3 ln (x) = 3

32 = 10 lo g_{10} (x)

What is the answer to log_{3}(x)+3log_{x}(3)=4 ?
The answer to log_{3}(x)+3log_{x}(3)=4 is x=27,x=3
Solve for x: log_{3}(x)+3log_{x}(3)=4
The solution is x=27,x=3