Question

If log (5x-9) - log (x+3)= log 2 then x= ?​

Answer 1

Answer:

The value of x is 5.

Explanation:

Given equation : \log (5x-9)-\log (x+3)= \log2log(5x−9)−log(x+3)=log2 (1)

According to the properties of logarithm , \log a-\log b=\log \dfrac{a}{b}loga−logb=log

b

a

So , \log (5x-9)-\log (x+3)=\log(\dfrac{5x-9}{x+3})log(5x−9)−log(x+3)=log(

x+3

5x−9

)

Put this in (1) , we get

\log(\dfrac{5x-9}{x+3}) =\log 2log(

x+3

5x−9

)=log2

\Rightarrow\ \dfrac{5x-9}{x+3}=2⇒

x+3

5x−9

=2 [ if \log a=\log b\Rightarrow\ a=bloga=logb⇒ a=b ]

\Rightarrow\ 5x-9=2(x+3)⇒ 5x−9=2(x+3)

\Rightarrow\ 5x-9=2x+6⇒ 5x−9=2x+6

\Rightarrow\ 5x-2x=6+9⇒ 5x−2x=6+9

\Rightarrow\ 3x=15⇒ 3x=15

\Rightarrow\ x=5⇒ x=5

Hence, the value of x is 5.

Step-by-step explanation:

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