Question

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

Answer 1

`log (x+2)+log\,2=log\,28` is required lograthmic equation.

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,

`log (x+2)+log\,2=log\,28`

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

`log\,((x+2)*2)=log\,28` (using lograthmic rule,
`log\,m* n=log\,m+log\,n`)

⇒ 2 × ( x + 2 ) = 28 (using lograthmic rule,
`log_(a)\,x=log_(a)\,y \implies x=y` )

⇒ 2x + 4 = 28

⇒ 2x = 28 - 4 (transposing 4 to RHS)

⇒ 2x = 24 (transposing 2 to RHS)

⇒
`x=(24)/(2)`

⇒ x = 12

Therefore,
`log (x+2)+log\,2=log\,28` is required lograthmic equation.

Answer 2

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=㏒
`10^(12)`

As log has base 10,

So, x=㏒
`10^(12)`=12

So, logarithmic equation like x=log
`10^(12)` has same solution as x-4=2³