Question 65919
Solve for x:
{{{4 = ln(sqrt(x-2))+2}}} Subtract 2 from both sides.
{{{2 = ln(sqrt(x-2))}}} Rewrite the right side in exponential form.
{{{2 = ln(x-2)^(1/2)}}}  Apply the power rule for logarithms.
{{{2 = (1/2)ln(x-2)}}} Multiply both sides by 2.
{{{ln(x-2) = 4}}} Rewrite this in exponential form.
{{{x-2 = e^4}}} Add 2 to both sides.
{{{x = e^4+2}}} Evaluate.
{{{x = 54.5982+2}}}
{{{x = 56.5982}}}  Approximately.

Check:
{{{4 = ln(sqrt(56.5982 - 2))+2}}}
{{{4 = ln(sqrt(54.5982))+2}}} Use your calculator to evaluate.
{{{4 = 2.0000+2}}}
{{{4 = 4}}}