If log3. 18+log3. 3-log3. x=3

Question

asked Nov 17, 2022 160k views

2 Answers

Rolf Carlson · Answer 1 · 2022-11-22T03:15:58+0000

Given:

The equation is

$\log_318+\log_33-\log_3x=3$

To find:

The solution for the given equation.

Solution:

We have,

$\log_318+\log_33-\log_3x=3$

Using the properties of logarithm, we get

$\log_3(18* 3)-\log_3x=3$
$\left[\because \log(ab)=\log a+\log b\right]$

$\log_3(54)-\log_3x=3$

$\log_3\left((54)/(x)\right)=3$
$\left[\because \log((a)/(b))=\log a-\log b\right]$

(54)/(x)=3^3
$[\because \log_ab=x\Leftrightarrow b=a^x]$

On further simplification, we get

(54)/(x)=27

(54)/(27)=x

2=x

Therefore, the value of x is 2.