Question

How do you solve for x in `-5 = log _2 x`?

Answer 1

`x=1/32`

Explanation:

We start with `-5=log_2x`. Now, we can rewrite a logarithm as an exponentiation equation, like this: `color(red)(y)=color(blue)(b)^(color(green)(x)` becomes `log_color(blue)(b)color(red)(y)=color(green)(x)` and vice versa. So, `log_color(blue)(2)color(red)(x)=color(green)(-5)` becomes `color(red)(x)=color(blue)(2)^(color(green)(-5)`.

And if we solve `2^-5` we get `x=1/32` or `.03125`.