What is the answer to 2log_{3}(x)=4+6log_{x}(3) ?

The answer to 2log_{3}(x)=4+6log_{x}(3) is x=27,x= 1/3

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2log_{3}(x)=4+6log_{x}(3)

2 lo g_{3} (x) = 4 + 6 lo g_{x} (3)

x = 27, x = \frac{1}{3}

Solution steps

2 lo g_{3} (x) = 4 + 6 lo g_{x} (3)

Divide both sides by

2

\frac{2 lo g _{3} ( x )}{2} = \frac{4}{2} + \frac{6 lo g _{x} ( 3 )}{2}

Simplify

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

Apply log rules

lo g_{3} (x) = 2 + \frac{3}{lo g _{3} ( x )}

Rewrite the equation with

lo g_{3} (x) = u

u = 2 + \frac{3}{u}

Solve

u = 2 + \frac{3}{u} : u = 3, u = - 1

u = 3, u = - 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 3 : x = 27

Solve

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

x = 27, x = \frac{1}{3}

Verify Solutions:

x = 27

True

, x = \frac{1}{3}

True

The solutions are

x = 27, x = \frac{1}{3}

lo g_{6} ((x + 7) (x - 2)) = 2

12 lo g_{x} (5) = 3 lo g_{5} (x)

lo g_{10} (4 x + 1) = lo g_{10} (x + 2)

lo g_{10} (2 x - 100) = 3

0.69 = ln (y)

What is the answer to 2log_{3}(x)=4+6log_{x}(3) ?
The answer to 2log_{3}(x)=4+6log_{x}(3) is x=27,x= 1/3
Solve for x: 2log_{3}(x)=4+6log_{x}(3)
The solution is x=27,x= 1/3