What is the answer to log_{6}(x^3)-2log_{x}(6)=1 ?

The answer to log_{6}(x^3)-2log_{x}(6)=1 is x=6,x= 1/(6^{2/3)}

Solve for x: log_{6}(x^3)-2log_{x}(6)=1

The solution is x=6,x= 1/(6^{2/3)}

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

x = 6, x = \frac{1}{6 ^{\frac{2}{3}}}

Decimal Notation

x = 6, x = 0.30285 \dots

Solution steps

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

Apply log rules

3 lo g_{6} (x) - \frac{2}{lo g _{6} ( x )} = 1

Rewrite the equation with

lo g_{6} (x) = u

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

Solve

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

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

Substitute back

u = lo g_{6} (x),

solve for

x

Solve

lo g_{6} (x) = 1 : x = 6

Solve

lo g_{6} (x) = - \frac{2}{3} : x = \frac{1}{6 ^{\frac{2}{3}}}

x = 6, x = \frac{1}{6 ^{\frac{2}{3}}}

Verify Solutions:

x = 6

True

, x = \frac{1}{6 ^{\frac{2}{3}}}

True

The solutions are

x = 6, x = \frac{1}{6 ^{\frac{2}{3}}}

lo g_{2} (5 x + 4) = 1

lo g_{5} (5 x) + lo g_{7} (7) = 9

5.54 = 0.67 lo g_{10} (0.03 x)

lo g_{10} (x) = 1891

n, lo g_{2} (n) = 1

What is the answer to log_{6}(x^3)-2log_{x}(6)=1 ?
The answer to log_{6}(x^3)-2log_{x}(6)=1 is x=6,x= 1/(6^{2/3)}
Solve for x: log_{6}(x^3)-2log_{x}(6)=1
The solution is x=6,x= 1/(6^{2/3)}