What is the answer to log_{3}(x)+2log_{x}(9)=5 ?

The answer to log_{3}(x)+2log_{x}(9)=5 is x=81,x=3

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log_{3}(x)+2log_{x}(9)=5

lo g_{3} (x) + 2 lo g_{x} (9) = 5

x = 81, x = 3

Solution steps

lo g_{3} (x) + 2 lo g_{x} (9) = 5

Apply log rules

lo g_{3} (x) + \frac{4}{lo g _{3} ( x )} = 5

Rewrite the equation with

lo g_{3} (x) = u

u + \frac{4}{u} = 5

Solve

u + \frac{4}{u} = 5 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 4 : x = 81

Solve

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

x = 81, x = 3

Verify Solutions:

x = 81

True

, x = 3

True

The solutions are

x = 81, x = 3

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

ln (ln (x)) = 9

ln (a) = 1 - \frac{1}{a}

lo g_{x} (4) = 9

x, - 2 ln (x) = ln (u)

What is the answer to log_{3}(x)+2log_{x}(9)=5 ?
The answer to log_{3}(x)+2log_{x}(9)=5 is x=81,x=3
Solve for x: log_{3}(x)+2log_{x}(9)=5
The solution is x=81,x=3