Question

How do you solve `2^{x + 6}=32`?

Answer 1

`x=-1`

Explanation:

It really is an advantage to know all the powers up to 1000.
It makes any questions on logs or exponential equations so much easier to do!

You should recognise 32 as being a power of 2. If you are not sure which power it is, divide by 2 again and again to find the prime factors. The clue for this is that the other base in the equation is 2.

`2xx2xx2xx2xx2= 2^5 =32`

In solving an exponential equation, try to get either the bases or the indices the same.

`2^x+6 = 32" "rarr` can be written as `2^x+6 = 2^5`

If the bases of the equation are equal, the indices must be equal.

`:. x+6= 5`

`x = 5-6`

`x=-1`