Given that \(\log_{2} y^{\frac{1}{2}} = \log_{5} 125\), find the value of y.
Question 1 Report
Given that \(\log_{2} y^{\frac{1}{2}} = \log_{5} 125\), find the value of y.
Answer Details
We can simplify the left side of the equation as follows:
$$\log_{2} y^{\frac{1}{2}} = \frac{1}{2}\log_{2} y$$
Similarly, we can simplify the right side of the equation as follows:
$$\log_{5} 125 = \log_{5} 5^3 = 3\log_{5} 5 = 3$$
So we have:
$$\frac{1}{2}\log_{2} y = 3$$
Multiplying both sides by 2, we get:
$$\log_{2} y = 6$$
Using the definition of logarithms, we can write this as:
$$2^6 = y$$
Simplifying, we get:
$$y = 64$$
Therefore, the value of y is 64.
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning