Solve the following: ( x + 1) + ( x - 1) = 11 + 2 3 - Vidyadip

Question

Solve the following:$\log ( x + 1) + \log ( x - 1) = \log 11 + 2 \log 3$

✓

Answer

$\log ( x + 1) + \log ( x - 1) = \log 11 + 2 \log 3$
$\Rightarrow \log [(x + 1)(x - 1)] = \log 11 + \log 3^2$
$\Rightarrow \log {x^2 - 1} = \log (11.9)$
$\Rightarrow \log {x^2 - 1} = \log99$
$\Rightarrow x^2 - 1 = 99$
$\Rightarrow x^2 = 100$
So, $x = 10$ or $-10$
Negative value is rejected
So, $x = 10.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[3 marks sum]" from Logarithms→Logarithms — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

Using ruler and compasses only, construct a trapezium $\text{ABCD}$, in which the parallel sides $AB$ and $D$ Care $3.3 \ cm$ apart; $AB = 4.5\ cm, \angle A = 120^o BC = 3.6 \ cm$ and $\angle B$ is obtuse.

A copper wire when bent in the form of a square encloses an area of 272.25 $cm ^2$. If the same wire is bent into the form of a circle, what will be the area enclosed by the wire?

Factorise : $25(2a - b)^2- 81b^2$

What are rational numbers? Give ten examples.

The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle. Also, find the cost of cultivating the field at ₹ 24.60 per 100$m ^2$.

Factorise : $a^2+b^2-c^2-d^2+2 a b-2 c d$

What number increased by $15\%$ of itself gives $2921$?

Solve for $x : \frac{\log 125}{\log 5}=\log x$

Prove that : $x^2+ y^2 + z^2 - xy - yz - zx$ is always positive.

If $\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-b \sqrt{3}$, find the values of $a$ and $b$.