#1**+2 **

2^{2x+3}=14 Take log of both sides

(2x+3) Log 2 = log 14 solve for 'x'

x = (log 14/log2 -3 )/2 = .403677461 Then 2^x = 1.322876

ElectricPavlov
Apr 19, 2018

#3**+2 **

2^{(2x+3)}=14

The first thing you do is take a log base 2 of both sides, as exponentials and logarithms are inverses. I got the base of 2 from what the 2x+3 is raised to, which is a 2.

\(log_2(2^{2x+3})=log_2(14)\)

Since the base of the logarithm and the base of the exponential are the same, they cancel, leaving only 2x+3.

\(2x+3=log_2(14)\)

Subtract 3 from both sides.

\(2x=log_2(14)-3\)

Divide by 2

\(x=\frac{log_2(14)-3}{2}\)

\(x=0.403677461\)

So, 2^{x} is equivalent to \(2^{0.403677461}\).

\(2^{0.403677461}=1.322876\)

So, ElectricPavlov is right about the final answer, but I wanted to reiterate the steps in a little more detail, just for clarity's sake.

AdamTaurus
Apr 19, 2018