Question:
Evaluate: \( 8^{\log_5 5} \)
Evaluate: \( 8^{\log_5 5} \)
Show Hint
N/A
Updated On: Apr 23, 2025
- \( \log_5 25 \)
- 120
- 125
- \( \log_5 15 \)
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
\[ 8^{\log_5 5} = (2^3)^{\log_5 5} = 2^{3 \cdot \log_5 5} \] \[ = 2^{\log_5 (5^3)} = 2^{\log_5 125} \] Now apply the identity \( a^{\log_b b^k} = k \Rightarrow 2^{\log_5 125} = 125 \)
Was this answer helpful?
0
0
Top Questions on Algebra
The relationship between two variables \( x \) and \( y \) is given by \( x + py + q = 0 \) and is shown in the figure. Find the values of \( p \) and \( q \). Note: The figure shown is representative.
- What is the value of \( \left( \frac{3^{81}}{27^4} \right)^{\frac{1}{3}} \)?
- Which one of the following mathematical structure forms a group?
- The integral domain of which cardinality is not possible:
A. 5
B. 6
C. 7
D. 10 - If $ x + \frac{1}{x} = 2 \cos \theta $, find the value of \[ x^5 + \frac{1}{x^5} \] in terms of $\theta$.
View More Questions
Questions Asked in COMEDK UGET exam
- Given that the freezing point of benzene is $ 5.48^\circ C $ and its $ K_f $ value is $ 5.12^\circ C/m $, what would be the freezing point of a solution of 20 g of propane in 400 g of benzene?
- COMEDK UGET - 2024
- Colligative Properties
200 ml of an aqueous solution contains 3.6 g of Glucose and 1.2 g of Urea maintained at a temperature equal to 27$^{\circ}$C. What is the Osmotic pressure of the solution in atmosphere units?
Given Data R = 0.082 L atm K$^{-1}$ mol$^{-1}$
Molecular Formula: Glucose = C$_6$H$_{12}$O$_6$, Urea = NH$_2$CONH$_2$- COMEDK UGET - 2024
- Colligative Properties
- An inorganic compound W undergoes the following reactions: $ W + \text{Na}_2\text{CO}_3 \xrightarrow{\text{O}_2 / \text{heat}} X + H^+ \xrightarrow{} Y(s) $ $ Y(aq) + \text{KCl} (aq) \xrightarrow{} Z(s) $ Z appears in the form of orange crystals and is used as an oxidising agent in acid medium. Identify the compound W.
- COMEDK UGET - 2024
- coordination compounds
- A current of 3.0 A is passed through 750 ml of 0.45 M solution of CuSO₄ for 2 hours with a current efficiency of 90\%. If the volume of the solution is assumed to remain constant, what would be the final molarity of CuSO₄ solution?
- COMEDK UGET - 2024
- Solutions
- For a reaction $ 5X + Y \to 3Z $, the rate of formation of Z is $ 2.4 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} $. Calculate the average rate of disappearance of X.
- COMEDK UGET - 2024
- Stoichiometry and Stoichiometric Calculations
View More Questions