What is the answer to log_{10}(-2x)log_{10}(6)=1 ?

The answer to log_{10}(-2x)log_{10}(6)=1 is x=-2^{(1-log_{10}(6))/(log_{10)(6)}}*5^{1/(log_{10)(6)}}

Solve for x: log_{10}(-2x)log_{10}(6)=1

The solution is x=-2^{(1-log_{10}(6))/(log_{10)(6)}}*5^{1/(log_{10)(6)}}

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

x = - 2^{\frac{1 - l o g _{10} ( 6 )}{l o g _{10} ( 6 )}} \cdot 5^{\frac{1}{l o g _{10} ( 6 )}}

Decimal

x = - 9.63978 \dots

Solution steps

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

Divide both sides by

lo g_{10} (6)

lo g_{10} (- 2 x) = \frac{1}{lo g _{10} ( 6 )}

Apply log rules

- 2 x = 1 0^{\frac{1}{l o g _{10} ( 6 )}}

Solve

- 2 x = 1 0^{\frac{1}{l o g _{10} ( 6 )}} : x = - 2^{\frac{1 - l o g _{10} ( 6 )}{l o g _{10} ( 6 )}} \cdot 5^{\frac{1}{l o g _{10} ( 6 )}}

x = - 2^{\frac{1 - l o g _{10} ( 6 )}{l o g _{10} ( 6 )}} \cdot 5^{\frac{1}{l o g _{10} ( 6 )}}

Verify Solutions:

x = - 2^{\frac{1 - l o g _{10} ( 6 )}{l o g _{10} ( 6 )}} \cdot 5^{\frac{1}{l o g _{10} ( 6 )}}

True

The solution is

x = - 2^{\frac{1 - l o g _{10} ( 6 )}{l o g _{10} ( 6 )}} \cdot 5^{\frac{1}{l o g _{10} ( 6 )}}

lo g_{x} (729) = 2

lo g_{4} (2 x - 5) = 0.5

3 lo g_{10} (5 x) = 15

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

ln (\frac{c x}{ab + c}) = b + c

What is the answer to log_{10}(-2x)log_{10}(6)=1 ?
The answer to log_{10}(-2x)log_{10}(6)=1 is x=-2^{(1-log_{10}(6))/(log_{10)(6)}}*5^{1/(log_{10)(6)}}
Solve for x: log_{10}(-2x)log_{10}(6)=1
The solution is x=-2^{(1-log_{10}(6))/(log_{10)(6)}}*5^{1/(log_{10)(6)}}