Question

How do you solve `(1/2)^x=32`?

Answer 1

`x=-5`

Explanation:

`(1/2)^x=32`

there are `2` ways of solving this:

`1)`
convert to logarithmic form:

`a^m=n -> log_a(n)=m`

`(1/2)x=32 -> log_(1/2)(32)=x`

`log_(1/2)(32)=log_0.5(32)`

enter into a calculator:

`log_0.5(32)= -5`

`x=-5`

`2)`

laws of indices:

`a^-m = 1/(a^m)`

`(a^m)^n=a^(mn)`

convert `(1/2)` and `32` to powers of `2`:

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

`32 = 2^5`

`(1/2)^x=32`

`(2^-1)^x=2^5`

`2^(-1 * x) = 2^5`

`-1*x = 5`

`-x = 5`

divide by `-1`:

`x = -5`