what logarithmic equation has the same solution as x-4=2^3

• FelisFelis:

  What logarithmic equation has the same solution as x-4=2^3

  Solution:

  x-4=2³

  x-4=2*2*2

  x-4=8

  TO solve for x, Let us add 4 on both sides

  x-4+4=8+4

  x+0=12

  So, x=12

  But, x=12 is not a logarithmic equation and there are no options

  So, an equation like, x=㏒ [tex] 10^{12} [/tex]

  As log has base 10,

  So, x=㏒ [tex] 10^{12} [/tex]=12

  So, logarithmic equation like x=log [tex] 10^{12} [/tex] has same solution as x-4=2³

• aquialaska:

  Answer:

  [tex]log (x+2)+log\,2=log\,28[/tex] is required lograthmic equation.

  Step-by-step explanation:

  Given: Given equation, x - 4 = 2³

  To find: Logarithmic function whose solution is same as given equation.

  First we find the solution of given Equation.

  consider,

  x - 4 = 2³

  x - 4 = 8        ( ∵ 2³ = 2×2×2 = 8 )

  x = 8 + 4       ( Transposing 4 to RHS )

  x = 12

  Now we find the logarithmic equation whose solution is also x = 12.

  ( There exist many such equations )

  Lets say one of them is,

  [tex]log (x+2)+log\,2=log\,28[/tex]

  Now we find its solution to check if it is same or not.

  [tex]log\,((x+2)\times2)=log\,28[/tex]   (using lograthmic rule,[tex]log\,m\times n=log\,m+log\,n[/tex])

  ⇒ 2 × ( x + 2 ) = 28  (using lograthmic rule, [tex]log_{a}\,x=log_{a}\,y \implies x=y[/tex] )

  ⇒ 2x + 4 = 28

  ⇒ 2x = 28 - 4     (transposing 4 to RHS)

  ⇒ 2x = 24          (transposing 2 to RHS)

  ⇒ [tex]x=\frac{24}{2}[/tex]

  ⇒ x = 12

  Therefore, [tex]log (x+2)+log\,2=log\,28[/tex] is required lograthmic equation.