What is the answer to 3log_{x}(3)=8-4log_{3}(x) ?

The answer to 3log_{x}(3)=8-4log_{3}(x) is x=sqrt(3),x=3sqrt(3)

Solve for x: 3log_{x}(3)=8-4log_{3}(x)

The solution is x=sqrt(3),x=3sqrt(3)

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3 lo g_{x} (3) = 8 - 4 lo g_{3} (x)

x = 3, x = 33

Decimal Notation

x = 1.73205 \dots, x = 5.19615 \dots

Solution steps

3 lo g_{x} (3) = 8 - 4 lo g_{3} (x)

Apply log rules

\frac{3}{lo g _{3} ( x )} = 8 - 4 lo g_{3} (x)

Rewrite the equation with

lo g_{3} (x) = u

\frac{3}{u} = 8 - 4 u

Solve

\frac{3}{u} = 8 - 4 u : u = \frac{1}{2}, u = \frac{3}{2}

u = \frac{1}{2}, u = \frac{3}{2}

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = \frac{1}{2} : x = 3

Solve

lo g_{3} (x) = \frac{3}{2} : x = 33

x = 3, x = 33

Verify Solutions:

x = 3

True

, x = 33

True

The solutions are

x = 3, x = 33

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

3 ln (x) = ln (216)

5 = lo g_{4} (x) + lo g_{4} (x) + 1

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

lo g_{a} (- x) - lo g_{a} (2 - x) = 2

What is the answer to 3log_{x}(3)=8-4log_{3}(x) ?
The answer to 3log_{x}(3)=8-4log_{3}(x) is x=sqrt(3),x=3sqrt(3)
Solve for x: 3log_{x}(3)=8-4log_{3}(x)
The solution is x=sqrt(3),x=3sqrt(3)