Question

How do you solve `10^{x + 1} = 10^{2x - 11}`?

Answer 1

`x = 12`

Explanation:

In an exponential equation like this one, try to have either the bases the same, or the indices (or exponents ) the same.

In this case the bases are already the same! GREAT!

Because it is an equation, if the bases are equal then the indices must be equal as well.

We can write an equation and solve it for `x`

`color(white)(xxxxxxxxxxxx)color(red)(10)^color(blue)(x+1) = color(red)(10)^color(blue)(2x-11)`

`color(white)(xxxxxxxxxxxx)color(blue)(x+1 = 2x-11)`

`color(white)(xxxxxxxxxxxx)1+11 = 2x-x`

`color(white)(xxxxxxxxxxxxxxx)12 = x`