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

The answer to log_{3}(x)log_{9}(x)=2 is x=9,x= 1/9

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

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

x = 9, x = \frac{1}{9}

Decimal Notation

x = 9, x = 0.11111 \dots

Solution steps

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

Apply log rules

2 lo g_{9} (x)^{2} = 2

Rewrite the equation with

lo g_{9} (x) = u

2 u^{2} = 2

Solve

2 u^{2} = 2 : u = 1, u = - 1

u = 1, u = - 1

Substitute back

u = lo g_{9} (x),

solve for

x

Solve

lo g_{9} (x) = 1 : x = 9

Solve

lo g_{9} (x) = - 1 : x = \frac{1}{9}

x = 9, x = \frac{1}{9}

Verify Solutions:

x = 9

True

, x = \frac{1}{9}

True

The solutions are

x = 9, x = \frac{1}{9}

lo g_{10} (x) = 3.4151

2 \cdot ln (\frac{( 3 x )}{( x )}) - ln (x + 1) = 2

lo g_{10} (x + 2 7^{l o g_{3} (2)}) = 1

d^{2} + d + 1 = lo g_{10} (x)

lo g_{3} (1 - 6 x) = lo g_{3} (17 - x^{2})

What is the answer to log_{3}(x)log_{9}(x)=2 ?
The answer to log_{3}(x)log_{9}(x)=2 is x=9,x= 1/9
Solve for x: log_{3}(x)log_{9}(x)=2
The solution is x=9,x= 1/9