What is the answer to (log_{3}(x))^2=log_{9}(x) ?

The answer to (log_{3}(x))^2=log_{9}(x) is x=sqrt(3),x=1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(log_{3}(x))^2=log_{9}(x)

(lo g_{3} (x))^{2} = lo g_{9} (x)

x = 3, x = 1

Decimal Notation

x = 1.73205 \dots, x = 1

Solution steps

(lo g_{3} (x))^{2} = lo g_{9} (x)

Apply log rules

4 lo g_{9} (x)^{2} = lo g_{9} (x)

Rewrite the equation with

lo g_{9} (x) = u

4 u^{2} = u

Solve

4 u^{2} = u : u = \frac{1}{4}, u = 0

u = \frac{1}{4}, u = 0

Substitute back

u = lo g_{9} (x),

solve for

x

Solve

lo g_{9} (x) = \frac{1}{4} : x = 3

Solve

lo g_{9} (x) = 0 : x = 1

x = 3, x = 1

Verify Solutions:

x = 3

True

, x = 1

True

The solutions are

x = 3, x = 1

lo g_{x} (144) = 2

x + ln (x) = 0

ln (y) + 1 = 0

ln (5 x + 3) = 6

ln (5 x) - 2 ln (x^{2}) = 0

What is the answer to (log_{3}(x))^2=log_{9}(x) ?
The answer to (log_{3}(x))^2=log_{9}(x) is x=sqrt(3),x=1
Solve for x: (log_{3}(x))^2=log_{9}(x)
The solution is x=sqrt(3),x=1