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

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,

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

  (using lograthmic rule,)

⇒ 2 × ( x + 2 ) = 28  (using lograthmic rule, )

⇒ 2x + 4 = 28

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

⇒ 2x = 24          (transposing 2 to RHS)

⇒

⇒ x = 12

Therefore, is required lograthmic equation.