Question

Please help! I’ve see a couple a different answers and I’m getting even more confused.>>Consider the equation log(3x-1)=log28. Explain why 3x-1 is not equal to 8. Describe the steps you would take to solve the equation, and state what 3x-1 is equal to.

Answer 1

Answer:

Consider the equation: $\log (3x-1) = \log_2 8$

Since, the functions: $\log (3x-1)$ has a base of 10 and $\log_2 8$ has a base of 2.

By logarithmic properties:

$\log_a x = \log_a y$

⇒$x = y$

Since, these logarithmic functions have different bases they does not satisfy the logarithmic properties

⇒$(3x-1) \neq 8$

Solve the equation:  $\log (3x-1) = \log_2 8$

By Properties of logarithmic:

$\log_a x^n = n \log _a x$

$\log_b b = 1$

$\log_b x = a$ ⇒ $x = b^a$

Using these properties to solve the given equation as shown below:

$\log (3x-1) = \log_2 2^3$

$\log (3x-1) =3 \log_2 2$

$\log (3x-1) = 3$

$(3x-1) = 10^3$

$(3x-1) = 1000$

Therefore, (3x -1) is equal to 1000