Respuesta :
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
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.
