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

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

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

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

x = 3, x = 1

Decimal Notation

x = 1.73205 \dots, x = 1

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{9} (x) = u

u = 4 u^{2}

Solve

u = 4 u^{2} : 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

6 ln (2 x - 7) - 6 = - 18

ln (x) = ln (4)

9.1 = - lo g_{10} (x)

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

lo g_{x} (0.01) = - 2

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