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

The answer to 2x+(((ln(x-2)))/2)-6=0 is x=3

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2x+(((ln(x-2)))/2)-6=0

2 x + (\frac{( ln ( x - 2 ) )}{2}) - 6 = 0

x = 3

Solution steps

2 x + (\frac{( ln ( x - 2 ) )}{2}) - 6 = 0

Move

2 x

to the right side

\frac{ln ( x - 2 )}{2} - 6 = - 2 x

Move

6

to the right side

\frac{ln ( x - 2 )}{2} = - 2 x + 6

Multiply both sides by

2

ln (x - 2) = - 4 x + 12

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (x - 2)} = e^{- 4 x + 12}

Simplify

e^{l n (x - 2)} : x - 2

x - 2 = e^{- 4 x + 12}

Solve

x - 2 = e^{- 4 x + 12} : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{e} (n) = ln (n)

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

lo g_{2} (x + 10) = 8

lo g_{10} (5 x) + lo g_{10} (3 x) = 1

4 ln (5 x - 8) - 14 = - 2

What is the answer to 2x+(((ln(x-2)))/2)-6=0 ?
The answer to 2x+(((ln(x-2)))/2)-6=0 is x=3
Solve for x: 2x+(((ln(x-2)))/2)-6=0
The solution is x=3