Question

How do you solve `2^(x-3)=32`?

Answer 1

`color(blue)(x=8)`

Explanation:

`2^(x-3)=32`

Notice:

`32=2^5`

Therefore:

`2^(x-3)=2^5`

Since both bases are equal, then both exponents are equal:

`:.`

`x-3=5`

`x=8`

Answer 2

`color(purple)(x = 8`

Explanation:

`2^(x - 3) = 32`

`2^(x - 3) = 2^5, " as " 32 = 2^5`

`(x - 3)cancel( log 2) =5 cancel(log 2), " taking log on both sides"`

`x - 3 = 5 " or " x = 8`

Answer 3

`x=8`

Explanation:

When bases are equal, so are the exponents. We can rewrite `32` as `2^5` to get

`2^(x-3)=2^5`

We have the same base, so let's equate the exponents:

`x-3=5`

Adding `3` to both sides gives us

`x=8`

Hope this helps!