Question
Evaluate the following without using tables $:\log 5 + \log 8 - 2 \log 2$
✓
Answer
Consider the given expression
$\log 5+\log 8-2 \log 2 \ldots . .\left[n \log _a m=\log _a m^n\right]$
$ =\log 5+\log 8 \times 8-\log 2^2 \ldots . .\left[n \log _a m=\log _a m^n\right]$
$ =\log 5 \times 8-\log 2^2$
$ =\log 40-\log 4$
$=\log \frac{40}{4} \ldots .\left[\log _{\mathrm{a}} \mathrm{m}-\log _{\mathrm{a}} \mathrm{n}=\log _{\mathrm{a}}\left(\frac{m}{n}\right)\right]$
$ =\log 10$
$ =1$
$\log 5+\log 8-2 \log 2 \ldots . .\left[n \log _a m=\log _a m^n\right]$
$ =\log 5+\log 8 \times 8-\log 2^2 \ldots . .\left[n \log _a m=\log _a m^n\right]$
$ =\log 5 \times 8-\log 2^2$
$ =\log 40-\log 4$
$=\log \frac{40}{4} \ldots .\left[\log _{\mathrm{a}} \mathrm{m}-\log _{\mathrm{a}} \mathrm{n}=\log _{\mathrm{a}}\left(\frac{m}{n}\right)\right]$
$ =\log 10$
$ =1$
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
Find the circumference and area of a circle of radius 15 cm. (Take $\pi$ = 3.14 )
→6 men and 8 boys can finish a piece of work in 14 days while 8 men and 12 boys can do it in 10 days. Find the time taken by one man alone and that by one boy alone to finish the work.
If two sides of a triangle are $8 \ cm$ and $13 \ cm,$ then the length of the third side is between $a \ cm$ and $b \ cm.$ Find the values of $a$ and $b$ such that $a$ is less than $b.$
→
Use the adjoining figure and write the values of :
(i) $\sin x^{\circ}$ (ii) $\cos y^{\circ}$
(iii) $3 \tan x^{\circ}-2 \sin y^{\circ}+4 \cos y^{\circ}$
$\left[\right.$ Hint. $\left.A B=\sqrt{A C^2-B C^2}.\right]$
The mean of the following data is 21.6. Find the value of p.
| xi | 6 | 12 | 18 | 24 | 30 | 36 |
| fi | 5 | 4 | p | 6 | 4 | 6 |
Each face of a cube has a perimeter equal to $32 \ cm$. Find its surface area and its volume.
→In the given figure, ABCP is a quadrant of a circle of radius 14 cm. With AC as diameter, a semi-circle is drawn. Find the area of the shaded region.
In the adjoining figure, CE is drawn parallel to DB to meet AB produced at E .
Prove that: $\operatorname{ar}($ quad. $A B C D)=\operatorname{ar}(\triangle D A E)$.
→Prove that: $\operatorname{ar}($ quad. $A B C D)=\operatorname{ar}(\triangle D A E)$.
Find the area of a circle circumscribing an equilateral triangle of side 15 cm. [Take pi = 3.141]
A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.