Math, asked by pradeepkatyura740, 11 months ago

Log (10x + 5) - log (x - 4) = log2​

Answers

Answered by rishu6845
4

Answer:

\boxed{\huge{x =  -  \dfrac{13}{8}}}

Step-by-step explanation:

\bold{Given}\longrightarrow \\ log(10x + 5) - log(x - 4) = log2

\bold{To \: find}\longrightarrow \\ value \: of \: x

\bold{Concept \: used}\longrightarrow \\ logx - logy = log \dfrac{x}{y}

\bold{Solution}\longrightarrow \\ log(10x + 5) - log(x - 4) = log2

 applying  \:  \\ \: logx - logy = log \dfrac{x}{y}

 =  >  log( \dfrac{10x + 5}{x - 4} )  = log2

 =  >  \dfrac{10x + 5}{x - 4}  = 2

 =  > 10x + 5 = 2 \: (x - 4)

 =  >  10x + 5 = 2x - 8

 =  > 10x - 2x =  - 8 - 5

 =  > 8x =  - 13

 =  > x =  -  \dfrac{13}{8}

Answered by JanviMalhan
71

Step-by-step explanation:

Log ( 10x + 5 ) - log ( x - 4 ) = 2

=> log ( 10 x + 5 ) - log ( x - 4 ) = log 100

=> log ( 10 x + 5 ) = log 100 + log ( x - 4 )

=> log ( 10 x + 5 ) = log 100 ( x - 4 )

TAKING ANTI LOGARITHM ON BOTH SIDES ,

=> 10x + 5 = 100 ( x - 4 )

=> 10x + 5 = 100x - 400

=> 405 = 90 x

=> x = 4.5

 \sf \: hope \: it \: helps \: uh

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