MHT CET · Maths · Limits

$\lim _{x \rightarrow 0}\left(\log _3 3 x\right)^{\log _x 8}=\ldots$

A $e^{\log _3 8}$
B $\log _8 3$
C $e^{\log _8 3}$
D $\log _3 8$

Verified Solution

Answer & Solution

Correct Answer

(A) $e^{\log _3 8}$

Step-by-step Solution

Detailed explanation

No Solution

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

The particular solution of the differential equation $y(1+\log x)=\left(\log x^x\right) \frac{d y}{d x}$, when $y(e)=e^2$ is

MHT CET 2021 Medium
The value of $\int_{0}^{\pi} x \sin ^{3} x d x$ is

MHT CET 2008 Medium
The domain of the real valued function $f (x) = \sqrt{\frac{x - 2}{3 - x}}$ is…

MHT CET 2019 Easy
For L. P. P, maximize $z = 4 x_{1} + 2 x_{2}$ subject to $3 x_{1} + 2 x_{2} \geq 9, x_{1} - x_{2} \leq 3, x_{1} \geq 0, x_{2} \geq 0$ has ….

MHT CET 2019 Hard
If $\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2},x, y, z>0, x y < 1$, then the value of
$x y+y z+z x=$

MHT CET 2020 Hard
If $X = (4^{n} - 3 n - 1 : n \in N)$ and $Y = \{9 (n - 1) : n \in N\}$ , then $X \cap Y =$

MHT CET 2018 Hard

Explore more questions on app

From MHT CET

$\mathrm{y}=\mathrm{e}^x(\mathrm{~A} \cos x+\mathrm{B} \sin x)$ is the solution of the differential equation

MHT CET 2025 Medium
What it the IUPAC name of following compounds?

MHT CET 2025 Medium
The cumulative distribution function of a discrete random variable X is given by

Then $\mathrm{E}\left(\mathrm{X}^2\right)=$

MHT CET 2024 Easy
In $Δ A B C,$ with the usual notations, if $s i n B s i n C = \frac{b c}{a^{2}},$ then the triangle is ….

MHT CET 2019 Easy
Calculate the number of moles of the gas having volume 2.5 liter at $300 \mathrm{~K}$ and $4.5 \mathrm{~atm}$ ? $\left(\mathrm{R}=0.0821 \mathrm{~atm} \mathrm{dm}^3 \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$

MHT CET 2022 Easy
What is the change in potential of following cell $\mathrm{Zn}(\mathrm{s})\left|\begin{array}{c}\mathrm{Zn} \mathrm{n}^{2+} \ 1 \mathrm{M}\end{array}\right| \begin{gathered}\mathrm{Pb}^{2+} \ 1 \mathrm{M}\end{gathered} \mid \mathrm{Pb}(\mathrm{s})$ if concentration of ions at anode is increased 10 times?

MHT CET 2022 Medium

Explore more questions on app

\(\lim _{x \rightarrow 0}\left(\log _3 3 x\right)^{\log _x 8}=\ldots\)

Answer & Solution

Step-by-step Solution

See the Complete Solution