Question

If log (5x-9)-log (x+3)= log2 then x=

Answer 1

Answer:

$log (5x-9)-log (x+3)= log2 \\ \therefore \: log \frac{(5x-9)}{(x+3)} = log2 \\ \therefore \: \frac{(5x-9)}{(x+3)} = 2 \\ \therefore \: (5x-9) = 2(x + 3) \\ \therefore \: 5x-9 = 2x + 6 \\ \therefore \: 5x-2x = 6 + 9 \\ \therefore \: 3x= 15\\ \therefore \: x= \frac{15}{3} \\ \huge \fbox{\therefore \: x=5}$

Answer 2

The value of x is 5.

Explanation:

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

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

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

Put this in (1) , we get

$\log(\dfrac{5x-9}{x+3}) =\log 2$  

$\Rightarrow\ \dfrac{5x-9}{x+3}=2$[ if $\log a=\log b\Rightarrow\ a=b$ ]

$\Rightarrow\ 5x-9=2(x+3)$

$\Rightarrow\ 5x-9=2x+6$

$\Rightarrow\ 5x-2x=6+9$

$\Rightarrow\ 3x=15$

$\Rightarrow\ x=5$

Hence, the value of x is 5.

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