Answer:
Consider the equation: [tex]\log (3x-1) = \log_2 8[/tex]
Since, the functions: [tex]\log (3x-1)[/tex] has a base of 10 and [tex]\log_2 8[/tex] has a base of 2.
By logarithmic properties:
[tex]\log_a x = \log_a y[/tex]
⇒[tex]x = y[/tex]
Since, these logarithmic functions have different bases they does not satisfy the logarithmic properties
⇒[tex](3x-1) \neq 8[/tex]
Solve the equation: [tex]\log (3x-1) = \log_2 8[/tex]
By Properties of logarithmic:
[tex]\log_a x^n = n \log _a x[/tex]
[tex]\log_b b = 1[/tex]
[tex]\log_b x = a[/tex] ⇒ [tex]x = b^a[/tex]
Using these properties to solve the given equation as shown below:
[tex]\log (3x-1) = \log_2 2^3[/tex]
[tex]\log (3x-1) =3 \log_2 2[/tex]
[tex]\log (3x-1) = 3[/tex]
[tex](3x-1) = 10^3[/tex]
[tex](3x-1) = 1000[/tex]
Therefore, (3x -1) is equal to 1000
