What is the answer to log_{6}(7)-log_{6}(2x)=1 ?

The answer to log_{6}(7)-log_{6}(2x)=1 is x= 7/12

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log_{6}(7)-log_{6}(2x)=1

lo g_{6} (7) - lo g_{6} (2 x) = 1

x = \frac{7}{12}

Decimal

x = 0.58333 \dots

Solution steps

lo g_{6} (7) - lo g_{6} (2 x) = 1

Move

lo g_{6} (7)

to the right side

- lo g_{6} (2 x) = 1 - lo g_{6} (7)

Divide both sides by

- 1

lo g_{6} (2 x) = - 1 + lo g_{6} (7)

Apply log rules

2 x = \frac{7}{6}

Solve

2 x = \frac{7}{6} : x = \frac{7}{12}

x = \frac{7}{12}

Verify Solutions:

x = \frac{7}{12}

True

The solution is

x = \frac{7}{12}

ln (2 x) = - \frac{1}{10}

lo g_{2} (8 x + 1) = 4

lo g_{10} (x^{4} - 4) - lo g_{10} (x^{2} + 2) = 0

2 lo g_{7} (x - 1) = 0

x, 5 x + 3 ln (x - 4) = 25

What is the answer to log_{6}(7)-log_{6}(2x)=1 ?
The answer to log_{6}(7)-log_{6}(2x)=1 is x= 7/12
Solve for x: log_{6}(7)-log_{6}(2x)=1
The solution is x= 7/12