Question

How do you solve `log2 x = log (x + 16) - 1`?

Answer 1

`x=16/19`

Explanation:

`1`. Start by bringing `log(x+16)` to the left side of the equation.

`log(2x)=log(x+16)-1`

`log(2x)-log(x+16)=-1`

`2`. Using the log property, `log_color(purple)b(color(red)m/color(blue)n)=log_color(purple)b(color(red)m)-log_color(purple)b(color(blue)n)`, simplify the equation.

`log((2x)/(x+16))=-1`

`3`. Convert to exponential form.

`10^(-1)=((2x)/(x+16))`

`4` Solve for `x`.

`1/10=((2x)/(x+16))`

`(x+16)/10=2x`

`x+16=20x`

`19x=16`

`color(green)(|bar(ul(color(white)(a/a)x=16/19color(white)(a/a)|)))`