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

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

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

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

x = 2 e^{\frac{e}{2}}

Decimal Notation

x = 7.78569 \dots

Solution steps

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

Move

ln (2)

to the right side

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

Apply log rules

\frac{x}{2} = e^{e^{1 - l n (2)}}

Multiply both sides by

2

\frac{x}{2} \cdot 2 = e^{e^{1 - l n (2)}} \cdot 2

Apply log rules

x = 2 e^{\frac{e}{2}}

Verify Solutions:

x = 2 e^{\frac{e}{2}}

True

The solution is

x = 2 e^{\frac{e}{2}}

- lo g_{10} (x) = 12.7

4 = ln (\frac{7}{7 + x})

lo g_{10} (\frac{1}{x}) = 7.22

5 lo g_{4} (x - 2) - 16 = - 16

lo g_{10} (\frac{1}{x}) = 7.87

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