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

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

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

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

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

Decimal Notation

x = 3, x = 0.03703 \dots

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

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

Solve

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

u = 1, u = - 3

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 1 : x = 3

Solve

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

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

Verify Solutions:

x = 3

True

, x = \frac{1}{27}

True

The solutions are

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

lo g_{2} (x) + lo g_{x} (8) = 4

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

x, 44 f = ln (x^{2} - 2 x)

2 ln (5 x + 8) - 17 = - 5

2 ln (x - 3) = ln (x) - ln (4)

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