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

The answer to log_{3}(x)=3-2log_{x}(3) is x=9,x=3

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

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

x = 9, x = 3

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

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

Solve

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

u = 2, u = 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Solve

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

x = 9, x = 3

Verify Solutions:

x = 9

True

, x = 3

True

The solutions are

x = 9, x = 3

- 0.15 = lo g_{10} (x)

lo g_{2} (x) = 8

5 = 10 lo g_{10} (x)

4 lo g_{3} (x) = lo g_{9} (x) + 2

0.45 = ln (y)

What is the answer to log_{3}(x)=3-2log_{x}(3) ?
The answer to log_{3}(x)=3-2log_{x}(3) is x=9,x=3
Solve for x: log_{3}(x)=3-2log_{x}(3)
The solution is x=9,x=3