What is the answer to 6(ln(2x)+1)=0 ?

The answer to 6(ln(2x)+1)=0 is x= 1/(2e)

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6(ln(2x)+1)=0

6 (ln (2 x) + 1) = 0

x = \frac{1}{2 e}

Solution steps

6 (ln (2 x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (2 x) + 1 = 0

Solve

ln (2 x) + 1 = 0 : x = \frac{1}{2 e}

Verify Solutions:

x = \frac{1}{2 e}

True

The solution is

x = \frac{1}{2 e}

lo g_{x} (8) = \frac{3}{2}

ln (x) = - a

3 lo g_{10} (2 y) = - 6

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

3 ln (x) - 1 = 0