HARD Logarithm equation ?

Question

how would i solve for x in this equation

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

(sqrt is square root)

it tried to natural log both sides but it just won't simplify out! question been nagging me for long time

any other ways to solve for x , pls help

thanks in advance

Answer 1

√(x) = 1 + ln (2+x)

remember that ln e = 1

√(x) = ln e + ln (2+x)

√(x) = ln e(2+x)

square both sides

x = ln 2e(2+x)

take e to power each side

e^x = 2e(2+x)

e^x = 4e + 2ex

here I get stuck, later perhaps.

.

Answer 2

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

the numeric answer is 14.44

But to solve with algebra is something else...

Answer 3

That equation is called transcendental, and can not be solved using algebra.  You might try graphing both sides, ie y=sqrt(x) and y=1+ln(2+x) and see if and where they intersect.