Question

Explain the process of solving the following equation: 4^x - 2 = 20

Answer 1

Hi,

$4^x-2=20\\ \Rightarrow\ 4^x=22\\ \Rightarrow\ x*ln(4)=ln(22)\\ \Rightarrow\ x= \dfrac{ln(22)}{ln(4)}\\\\ \Rightarrow\ \boxed{ x=2,2297158...\approx{2.23}}$
ln means natural log (neper's log)

Answer 2

This is an exponential equation:  4^x - 2 = 20.  First thing:  combine the -2 and the 20:  4^x = 22.

Next, take the logarithm (natural or common log) of both sides.  We get:

                                            log 22
x log 4 = log 22.  Then x = -----------  (answer).  You could, of course, evaluate
                                            log 4       this on a suitable calculator.