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

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

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

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

x = 27, x = 3

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

\frac{3}{u} + u = 4

Solve

\frac{3}{u} + u = 4 : 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 = 3

x = 27, x = 3

Verify Solutions:

x = 27

True

, x = 3

True

The solutions are

x = 27, x = 3

lo g_{x - 4} (4) = \frac{3}{2}

lo g_{10} (x) = 0.2

3 lo g_{2} (x + 4) - 5 = 10

a, x = lo g_{10} (a)

lo g_{5} (x + 3) - lo g_{5} (x - 1) = 1

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