Exponential and logarithmic equations

Question

log₅x+log₅(x+5)=6

 

There are two potential roots, A and B, where A≤B.

A=

B=

Is A actually a root? (yes/no)

Is B actually a root? (yes/no)

Answer 1

log₅x+log₅(x+5)=6

log₅(x(x+5))=6

x(x+5)=5⁶

x²+5x-5⁶=0

x_1,2=-(5±√(5²+4*5⁶))/2=-(5/2)(1±√(1+4*5⁴))=-(5/2)(1±√2501).

 

100*25=2500+1