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

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

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(ln(x)+1)/2 =ln(x)

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

x = e

Decimal Notation

x = 2.71828 \dots

Solution steps

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

Multiply both sides by

2

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

Simplify

ln (x) + 1 = ln (x) \cdot 2

Move

1

to the right side

ln (x) = ln (x) \cdot 2 - 1

Move

ln (x) 2

to the left side

- ln (x) = - 1

Divide both sides by

- 1

ln (x) = 1

Apply log rules

x = e

Verify Solutions:

x = e

True

The solution is

x = e

lo g_{10} (x) + lo g_{10} (x - 7) = 2

lo g_{2} (x) + lo g_{4} (x) = 3

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

lo g_{2} (x + 4) = 2 - lo g_{2} (x + 7)

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

What is the answer to (ln(x)+1)/2 =ln(x) ?
The answer to (ln(x)+1)/2 =ln(x) is x=e
Solve for x: (ln(x)+1)/2 =ln(x)
The solution is x=e