What is the answer to log_{3}(x)=log_{x}(27)+2 ?

The answer to log_{3}(x)=log_{x}(27)+2 is x=27,x= 1/3

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log_{3}(x)=log_{x}(27)+2

lo g_{3} (x) = lo g_{x} (27) + 2

x = 27, x = \frac{1}{3}

Decimal Notation

x = 27, x = 0.33333 \dots

Solution steps

lo g_{3} (x) = lo g_{x} (27) + 2

Apply log rules

lo g_{3} (x) = \frac{3}{lo g _{3} ( x )} + 2

Rewrite the equation with

lo g_{3} (x) = u

u = \frac{3}{u} + 2

Solve

u = \frac{3}{u} + 2 : 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 = \frac{1}{3}

x = 27, x = \frac{1}{3}

Verify Solutions:

x = 27

True

, x = \frac{1}{3}

True

The solutions are

x = 27, x = \frac{1}{3}

ln (x^{2} - 9) = 0

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

lo g_{2} (x + 1) = 4

ln (\frac{3}{t - 5}) = 1.92

ln (x - 2) = 0

What is the answer to log_{3}(x)=log_{x}(27)+2 ?
The answer to log_{3}(x)=log_{x}(27)+2 is x=27,x= 1/3
Solve for x: log_{3}(x)=log_{x}(27)+2
The solution is x=27,x= 1/3