If log5log5log2x=0, then the value of x is
32
125
625
25
Explanation for the correct answer:
The given expression can be written as log5log5log2x=0
Using the property of logarithms
loga1=0 for any real value of a we can write as
log5log5log2x=log51
⇒ log5log2x=1 [∵logma=logmb⇒a=b]
⇒ log2x=51=5 [∵logab=m⇒b=am]
⇒ log2x=5×1
⇒ log2x=5×log22 [∵logaa=1]
⇒ log2x=log225 [∵mlogab=logabm]
⇒ log2x=log232
⇒ x=32 [∵logma=logmb⇒a=b]
Hence, the value of x is 32.
Hence, option (A) i.e. 32 is the correct answer.