Question:
3 numbers are in GP therefore, their logarithms are in
3 numbers are in GP therefore, their logarithms are in
Show Hint
Logarithm converts geometric progression to arithmetic progression.
Updated On: Apr 23, 2026
- GP
- HP
- AP
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Formula / Definition}
\[ a, b, c \text{ in GP} \Rightarrow b^2 = ac \]
Step 2: Calculation / Simplification}
Take \(\log\): \(\log(b^2) = \log(ac)\)
\(2\log b = \log a + \log c\)
\(\log b = \frac{\log a + \log c}{2}\)
\(\therefore \log a, \log b, \log c\) are in AP.
Step 3: Final Answer
\[ \text{AP} \]
\[ a, b, c \text{ in GP} \Rightarrow b^2 = ac \]
Step 2: Calculation / Simplification}
Take \(\log\): \(\log(b^2) = \log(ac)\)
\(2\log b = \log a + \log c\)
\(\log b = \frac{\log a + \log c}{2}\)
\(\therefore \log a, \log b, \log c\) are in AP.
Step 3: Final Answer
\[ \text{AP} \]
Was this answer helpful?
0
0
Top MET Mathematics Questions
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- The equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution
- A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is
- Every group of order 7 is
- Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to
View More Questions
Top MET Ellipse Questions
- The center of the ellipse \( \frac{(x+1)^2}{9} + \frac{(y-2)^2}{4} = 1 \) is:
- The eccentricity of the ellipse \( 9x^{2} + 5y^{2} = 45 \) is:
- The center of the ellipse \( \frac{(x+1)^{2}}{9} + \frac{(y-2)^{2}}{4} = 1 \) is:
- If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is
- The number of real tangents that can be drawn to the ellipse $3x²+5y²=32$ passing through (3, 5) is
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions