Question

How do you solve `log_4x- log_4(x-1)= 1/2`?

Answer 1

`x=2`

Explanation:

`1`. Recall the log quotient rule: `log_color(red)b(color(blue)m/color(purple)n)=log_color(red)b(color(blue)m)-log_color(red)b(color(purple)n)`. Using the formula, rewrite the left side of the equation.

`log_4(x)-log_4(x-1)=1/2`

`log_4(x/(x-1))=1/2`

`2`. Rewrite the equation in exponential form.

`4^(1/2)=x/(x-1)`

`3`. Solve for `x`.

`2=x/(x-1)`

`x=2(x-1)`

`x=2x-2`

`color(green)(x=2)`