Question

3. Evaluate : log(root(x))/log(x+2)​

Answer 1

Answer:

For x≥1 (domain of the expression):

logx−−√=logx−−−−√

12logx=logx−−−−√

logx=2logx−−−−√

log2x=4logx

logx(logx−4)=0

logx=0∨logx=4

x=1∨x=b4

where b∈R+∖{1} is the base of the logarithm.

Therefore your equation has two solutions:

x=1, x=b4

Particular cases:

b=e : x=1, x=e4

b=10 : x=1, x=104