Given X= log^3/2 , Y= log^5/2
solve 1. log base2 power 25
2. log base2 power 6350
Solve them in terms of x and y
Answers
Answer:
please mark me as brainlist
Step-by-step explanation:
Given that log
2
(25
x+3
−1)=2+log
2
(5
x+3
+1)
⟹log
2
(5
2(x+3)
−1)−log
2
(5
x+3
+1)=2
⟹log
2
(
5
(x+3)
+1
5
2(x+3)
−1
)=2 (since, log(a−b)=log(
b
a
))
⟹
5
(x+3)
+1
5
2(x+3)
−1
=2
2
(since, log
a
x=b⟹a
b
=x)
⟹5
2(x+3)
−1=4(5
(x+3)
+1)
⟹(5
(x+3)
)
2
−1−4(5
(x+3)
)−4=0
Let t=5
(x+3)
⟹t
2
−4t−5=0
⟹t
2
−5t+t−5=0
⟹t(t−5)+1(t−5)=0
⟹(t−5)(t+1)=0
⟹t=5 or t=−1
But, 5
(x+3)
=−1 is not possible.
Therefore, 5
(x+3)
=5
Bases are equal. Therefore, powers are equated.
⟹x+3=1⟹x=−2
Was this answer helpful?
upvote
6
downvote
1
SIMILAR QUESTIONS
star-struck
Solve log
x
2.log
2x
2.log
2
4x>1
Hard
View solution
>
If A=log
2
log
2
log
4
256+2log
2
2, then A is equal to
Medium
View solution
>
View more
MORE FROM CHAPTER
Logarithm and Antilogarithm
View chapter
>
PRACTICE MORE QUESTIONS
Easy Questions
471 Qs
>
Medium Questions
471 Qs
>
Hard Questions
52 Qs
>
Enjoy a better exp