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

The answer to log_{3}(x)=9log_{x}(3) is x=27,x= 1/27

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log_{3}(x)=9log_{x}(3)

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

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

Decimal Notation

x = 27, x = 0.03703 \dots

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

u = \frac{9}{u}

Solve

u = \frac{9}{u} : u = 3, u = - 3

u = 3, u = - 3

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Solve

lo g_{3} (x) = - 3 : x = \frac{1}{27}

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

Verify Solutions:

x = 27

True

, x = \frac{1}{27}

True

The solutions are

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

6 + lo g_{3} (- 4 x) = 9

lo g_{3} (x^{2} - 3 x - 1) = 0

lo g_{2} (x - 5) = 3 - lo g_{2} (x - 7)

ln (x) + ln (x - 1) = ln (6)

lo g_{16} (x) = (lo g_{4} (x))^{2}

What is the answer to log_{3}(x)=9log_{x}(3) ?
The answer to log_{3}(x)=9log_{x}(3) is x=27,x= 1/27
Solve for x: log_{3}(x)=9log_{x}(3)
The solution is x=27,x= 1/27