What is the answer to log_{6}(x^2)2log_{6}(x)=1 ?

The answer to log_{6}(x^2)2log_{6}(x)=1 is x=sqrt(6),x= 1/(sqrt(6))

Solve for x: log_{6}(x^2)2log_{6}(x)=1

The solution is x=sqrt(6),x= 1/(sqrt(6))

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

x = 6, x = \frac{1}{6}

Decimal Notation

x = 2.44948 \dots, x = 0.40824 \dots

Solution steps

lo g_{6} (x^{2}) \cdot 2 lo g_{6} (x) = 1

Apply log rules

2 lo g_{6} (x) \cdot 2 lo g_{6} (x) = 1

Rewrite the equation with

lo g_{6} (x) = u

2 u \cdot 2 u = 1

Solve

2 u \cdot 2 u = 1 : u = \frac{1}{4}, u = - \frac{1}{4}

u = \frac{1}{4}, u = - \frac{1}{4}

Substitute back

u = lo g_{6} (x),

solve for

x

Solve

lo g_{6} (x) = \frac{1}{4} : x = 6

Solve

lo g_{6} (x) = - \frac{1}{4} : x = \frac{1}{6}

x = 6, x = \frac{1}{6}

Verify Solutions:

x = 6

True

, x = \frac{1}{6}

True

The solutions are

x = 6, x = \frac{1}{6}

0 = lo g_{2} (5 - x)

ln (x) = \frac{a}{3} + 1

lo g_{2} (x + 5) = 5 - lo g_{2} (x)

x, f x = lo g_{10} (x - 3)

lo g_{10} (6 - 2 x) = 1 + lo g_{10} (x)

What is the answer to log_{6}(x^2)2log_{6}(x)=1 ?
The answer to log_{6}(x^2)2log_{6}(x)=1 is x=sqrt(6),x= 1/(sqrt(6))
Solve for x: log_{6}(x^2)2log_{6}(x)=1
The solution is x=sqrt(6),x= 1/(sqrt(6))