Question

find x if log3(x-2)+log3x =1​

Answer 1

Answer:

We know that,

log

a

b=x⇒b=a

x

log

3

[log

2

(log

3

x)]=1

log

2

(log

3

x)=3

1

=3

log

3

x=2

3

=8

x=3

8

=6561.

Answer 2

Given

$\log 3(x-2) +\log3x =1$

To find :

The value of x

Solution:

Let  a=3(x-2) and 3x=b

Then the given equation is

$\log a +\log b=1\\\\\log(ab)= \log 10 ( \because \log 10=1)\\\\ab =10\\\\Punting\ values\, of\ a\ and \ b\\\\9x(3x-2)=10\\\\9x^2-18x-10=0\\\\\\Thus\\\\x= \frac{18 \pm \sqrt{324+360} }{18}$

$x= \frac{18\pm\sqrt{684} }{18} \\\\=\frac{ 18\pm6 \sqrt{19} }{18}\\\\=\frac{ 3\pm \sqrt{19} }{3}$

Answer:

$x=\frac{ 3\pm \sqrt{19} }{3}$

Formulas used

$1.\log a +\log b=\log ab\\\\2.Quatrain \ equation \ concept$