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
- \( \log_5 15 \)
Show 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 COMEDK UGET Mathematics Questions
- If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then
- $ \frac{1 -\tan^2 15^\circ}{1 + \tan^2 15^\circ} = $
- Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of $n$ is
- $1 + 3 + 5 + 7 + ... + 29 + 30 +31 + 32 + ... + 60 =$
- Let $f (x)$ and $g(x)$ be differentiable functions on (0, 2] such that $f"(x) - g"(x) = 0, f'(1) = 2g'(1) = 4, f(2) = 3g(2) = 9.$ Then $f (x)- g(x)$ at $ x = 3/2$ is
View More Questions
Top COMEDK UGET Algebra Questions
- If $2f(x^2) + 3f\left( \frac{1}{x^2} \right) = x^2 - 1$, for $x \in \mathbb{R} - \{0\}$, then $f(x^8)$ is equal to
- Using mathematical induction, the numbers \( a_n \)'s are defined by \( a_0 = 1 \), \( a_{n+1} = 3n^2 + n + a_n \), \( (n \geq 0) \). Then, \( a_n \) is equal to:
- If \( 49^n + 16n + P \) is divisible by 64 for all \( n \in \mathbb{N} \), then the least negative integral value of \( P \) is:
- Evaluate \( 3^n - 7n - 1 \) is divisible by:
- The digits of a three-digit number taken in an order are in geometric progression. If one is added to the middle digit, they form an arithmetic progression. If 594 is subtracted from the number, then a new number with the same digits in reverse order is formed. The original number is divisible by
Top COMEDK UGET Questions
- If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then
- A long hollow copper pipe carries a current. The magnetic field producted will be
- An ammeter reads 0 to 10 A. It has negligible resistance.To convert this into voltmeter to read upto 250 V, resistance to be used is
- Force of attraction or repulsion between two current carrying wires separated by a distance r is proportional to
- When a material is placed in a magnetic field B, a magnetic moment proportional tc B but in a direction opposite to B is induced. The material is
View More Questions