Question

How do you solve `5(2^x) = 3 - 2^(x+2)`?

Answer 1

`x = log_2(1/3)`

Explanation:

First of all, remember the power rule `a^n * a^m = a^(n+m)`, we will use it.

Let's transform the equation:

`color(white)(xxx)5 * 2^x = 3 - 2^(x+2)`

`<=> 5 * 2^x = 3 - 2^x * 2^2`

`<=> 5 * 2^x = 3 - 4 * 2^x`

... add `4 * 2^x` on both sides...

`<=> 9 * 2^x = 3`

... divide by `9` on both sides ...

`<=> 2^x = 1/3`

.. apply `log_2` on both sides...

`<=> x = log_2(1/3)`