What is the answer to 4log_{x}(3)+log_{3}(x)+5=0 ?

The answer to 4log_{x}(3)+log_{3}(x)+5=0 is x= 1/3 ,x= 1/81

Solve for x: 4log_{x}(3)+log_{3}(x)+5=0

The solution is x= 1/3 ,x= 1/81

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4 lo g_{x} (3) + lo g_{3} (x) + 5 = 0

x = \frac{1}{3}, x = \frac{1}{81}

Decimal Notation

x = 0.33333 \dots, x = 0.01234 \dots

Solution steps

4 lo g_{x} (3) + lo g_{3} (x) + 5 = 0

Apply log rules

\frac{4}{lo g _{3} ( x )} + lo g_{3} (x) + 5 = 0

Rewrite the equation with

lo g_{3} (x) = u

\frac{4}{u} + u + 5 = 0

Solve

\frac{4}{u} + u + 5 = 0 : u = - 1, u = - 4

u = - 1, u = - 4

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Solve

lo g_{3} (x) = - 4 : x = \frac{1}{81}

x = \frac{1}{3}, x = \frac{1}{81}

Verify Solutions:

x = \frac{1}{3}

True

, x = \frac{1}{81}

True

The solutions are

x = \frac{1}{3}, x = \frac{1}{81}

ln (\frac{1}{3} x + 2) = 2

ln (- x) = ln (\frac{1}{x})

ln (2 t + 1) = \frac{9}{4}

a, ln (a) + ln (b) = c

0 = 2 ln (x) + 2

What is the answer to 4log_{x}(3)+log_{3}(x)+5=0 ?
The answer to 4log_{x}(3)+log_{3}(x)+5=0 is x= 1/3 ,x= 1/81
Solve for x: 4log_{x}(3)+log_{3}(x)+5=0
The solution is x= 1/3 ,x= 1/81