Question

Problem 18
Solve for x : log 2 + log (x + 3) - log (3x - 5) = log 3
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Answer 1

Answer :

x = 3

Solution :

• Given : log2 + log(x + 3) - log(3x - 5) = log3

• To find : x = ?

We have ,

=> log2 + log(x + 3) - log(3x - 5) = log3

=> log[2•(x + 3)/(3x - 5)] = log3

=> 2•(x + 3)/(3x - 5) = 3

=> 2(x + 3) = 3(3x - 5)

=> 2x + 6 = 9x - 15

=> 9x - 2x = 6 + 15

=> 7x = 21

=> x = 21/7

=> x = 3

Hence , x = 3 .

Answer 2

$\tt { log \: 2 \: + log \: (x + 3) - log \: (3x \: - \: 5) \: = log \: 3}$

Therefore.

$\tt {=log \: [2 ( x + 3 )] - \:log\: (3x - 5) = \:log}$

$\tt { =log \: \frac{(2x + 6)}{(3x - 5)} = log \: 3}$

$\tt {= \frac{2x + 6}{3x - 5} = 3}$

$\tt {=2x + 6 = 9x - 15}$

$\tt {= - 7x = - 21}$

$\tt {x = 3}$