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

The answer to 4log_{4}(x)=log_{x}(4) is x=2,x= 1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 2, x = \frac{1}{2}

Decimal Notation

x = 2, x = 0.5

Solution steps

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

Apply log rules

4 lo g_{4} (x) = \frac{1}{lo g _{4} ( x )}

Rewrite the equation with

lo g_{4} (x) = u

4 u = \frac{1}{u}

Solve

4 u = \frac{1}{u} : u = \frac{1}{2}, u = - \frac{1}{2}

u = \frac{1}{2}, u = - \frac{1}{2}

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = \frac{1}{2} : x = 2

Solve

lo g_{4} (x) = - \frac{1}{2} : x = \frac{1}{2}

x = 2, x = \frac{1}{2}

Verify Solutions:

x = 2

True

, x = \frac{1}{2}

True

The solutions are

x = 2, x = \frac{1}{2}

x, ln (y) = 4 ln (x)

0.25 = lo g_{10} (x)

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

lo g_{\frac{1}{2}} (x) = - 2

lo g_{10} (2 x) + lo g_{10} (x) = 11

What is the answer to 4log_{4}(x)=log_{x}(4) ?
The answer to 4log_{4}(x)=log_{x}(4) is x=2,x= 1/2
Solve for x: 4log_{4}(x)=log_{x}(4)
The solution is x=2,x= 1/2