What is the answer to (3-log_{3}(x))log_{3x}(3)=1 ?

The answer to (3-log_{3}(x))log_{3x}(3)=1 is x=3

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(3-log_{3}(x))log_{3x}(3)=1

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

x = 3

Solution steps

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

Apply log rules

\frac{3 - lo g _{3} ( x )}{lo g _{3} ( 3 ) + lo g _{3} ( x )} = 1

Rewrite the equation with

lo g_{3} (x) = u

\frac{3 - u}{lo g _{3} ( 3 ) + u} = 1

Solve

\frac{3 - u}{lo g _{3} ( 3 ) + u} = 1 : u = 1

u = 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

ln (e^{2 x} + 3) = 2 x + ln (3)

lo g_{3} (2 x + 1) = - 1

lo g_{a} (32) = - \frac{5}{2}

3.5 = - lo g_{10} (c)

N, x = lo g_{a} (N)

What is the answer to (3-log_{3}(x))log_{3x}(3)=1 ?
The answer to (3-log_{3}(x))log_{3x}(3)=1 is x=3
Solve for x: (3-log_{3}(x))log_{3x}(3)=1
The solution is x=3