Question

Solve

Log(×-1)-log4=2

Answer 1

[AI-generated answer — Explain Bot]

To solve the equation log(x-1) - log4 = 2, we can apply the logarithmic properties to simplify the equation.

First, let's combine the two logarithms using the quotient rule of logarithms. According to this rule, when we subtract logarithms with the same base, we can rewrite the equation as the logarithm of the division of the arguments:

log((x-1) / 4) = 2

Next, we can rewrite the equation using the exponential form of logarithms. In exponential form, log base b of a equals c can be expressed as b raised to the power of c equals a.

(x-1) / 4 = 10 ^ 2

Since 10 ^ 2 equals 100, we can simplify further:

(x-1) / 4 = 100

To solve for x, we will isolate it by multiplying both sides of the equation by 4:

(x-1) = 400

Now, we can solve for x by adding 1 to both sides:

x = 401

Therefore, the solution to the equation log(x-1) - log4 = 2 is x = 401.