Question
Evaluate : $log_38 \div log_916$
✓
Answer
$\log _3 8 \div \log _9 16$
$ \Rightarrow \frac{\log _3 8}{\log _9 16}$
$ \Rightarrow \frac{\log _{10} 8}{\log _{10} 3} \times \frac{\log _{10} 9}{\log _{10} 16}$
$ \Rightarrow \frac{3 \log _{10} 2}{\log _{10} 3} \times \frac{2 \log _{10} 3}{4 \log _{10} 2}$
$ \Rightarrow \frac{3}{2}$
$ \Rightarrow \frac{\log _3 8}{\log _9 16}$
$ \Rightarrow \frac{\log _{10} 8}{\log _{10} 3} \times \frac{\log _{10} 9}{\log _{10} 16}$
$ \Rightarrow \frac{3 \log _{10} 2}{\log _{10} 3} \times \frac{2 \log _{10} 3}{4 \log _{10} 2}$
$ \Rightarrow \frac{3}{2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Convert decimals into a vulgar fraction in its lowest term:
$1.08$
→$1.08$
Find the value of: $\log _{0.1} 10$
→Without doing any actual division $, $ find which of the following rational numbers have terminating decimal representation : $\frac{7}{16}$
→Evaluate the following$: \frac{\sin 62^{\circ}}{\cos 28^{\circ}}$
→Factoriseusing the grouping method $:x^2+ y^2+ x + y + 2xy$
→If $\log 8=0.9030$, find the value of :
$\log 4$
→$\log 4$
Represent each of the following on the real line.
(i) $\sqrt{3}$
(ii) $\sqrt{5}$
(iii) $\sqrt{6}$
(iv) $\sqrt{10}$
→(i) $\sqrt{3}$
(ii) $\sqrt{5}$
(iii) $\sqrt{6}$
(iv) $\sqrt{10}$
$A B$ is a line segment. $A X$ and $B Y$ are two equal line segments drawn on opposite sides of $A B$ such that $A X \| Y B$. If $A B$ and $X Y$ intersect at $M$, prove that :
(i) $\triangle AMX \cong \triangle BMY$ (ii) AB and XY bisect each other at M .
→(i) $\triangle AMX \cong \triangle BMY$ (ii) AB and XY bisect each other at M .
Evaluate:
$\log \frac{81}{8}+2 \log \frac{2}{3}-3 \log \frac{3}{2}+\log \frac{3}{4}$
→$\log \frac{81}{8}+2 \log \frac{2}{3}-3 \log \frac{3}{2}+\log \frac{3}{4}$
A sum of ₹12,500 is deposited for $1 \frac{1}{2}$ years, compounded half yearly. It amounts to ₹13,000 at the end of first half year. Find:
(i) The rate of interest
(ii) The final amount. Give your answer correct to the nearest rupee.
→(i) The rate of interest
(ii) The final amount. Give your answer correct to the nearest rupee.