What is the answer to log_{x}(3)=log_{3}(9x^3) ?

The answer to log_{x}(3)=log_{3}(9x^3) is x=\sqrt[3]{3},x= 1/3

Solve for x: log_{x}(3)=log_{3}(9x^3)

The solution is x=\sqrt[3]{3},x= 1/3

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lo g_{x} (3) = lo g_{3} (9 x^{3})

Decimal Notation

x = 1.44224 \dots, x = 0.33333 \dots

Solution steps

lo g_{x} (3) = lo g_{3} (9 x^{3})

Apply log rules

\frac{1}{lo g _{3} ( x )} = lo g_{3} (9) + 3 lo g_{3} (x)

Rewrite the equation with

lo g_{3} (x) = u

\frac{1}{u} = lo g_{3} (9) + 3 u

Solve

\frac{1}{u} = lo g_{3} (9) + 3 u : u = \frac{1}{3}, u = - 1

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

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Verify Solutions:

True

, x = \frac{1}{3}

True

The solutions are

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

lo g_{3} (- 2 x + 13) = 1

2 lo g_{5} (9 x - 5) + 2 = - 4

ln (x) + 5 = 0

lo g_{2} (9 - x) = 3

What is the answer to log_{x}(3)=log_{3}(9x^3) ?
The answer to log_{x}(3)=log_{3}(9x^3) is x=\sqrt[3]{3},x= 1/3
Solve for x: log_{x}(3)=log_{3}(9x^3)
The solution is x=\sqrt[3]{3},x= 1/3