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

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Answer 1 · 2015-11-26T14:36:50

$x = log_2(1/3)$

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...

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

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