What is the answer to log_{4}(x)-2log_{x}(4)=1 ?

The answer to log_{4}(x)-2log_{x}(4)=1 is x=16,x= 1/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{4}(x)-2log_{x}(4)=1

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

x = 16, x = \frac{1}{4}

Decimal Notation

x = 16, x = 0.25

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{4} (x) = u

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

Solve

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

u = 2, u = - 1

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 2 : x = 16

Solve

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

x = 16, x = \frac{1}{4}

Verify Solutions:

x = 16

True

, x = \frac{1}{4}

True

The solutions are

x = 16, x = \frac{1}{4}

1 + ln (x) = ln (6)

lo g_{10} (x) 32 = 5

ln (\frac{1}{x}) = - 5

lo g_{10} (9 x) = lo g_{3} (3 x)

lo g_{3} (z) = - 5

What is the answer to log_{4}(x)-2log_{x}(4)=1 ?
The answer to log_{4}(x)-2log_{x}(4)=1 is x=16,x= 1/4
Solve for x: log_{4}(x)-2log_{x}(4)=1
The solution is x=16,x= 1/4