We have the question as
[tex]4^{x+6}=20[/tex]
Let us introduce logarithms to base 4 to both sides of the equation:
[tex]\log _44^{x+6}=\log _420[/tex]
Applying the law of logarithm that states
[tex]\log A^B=B\log A[/tex]
we have
[tex](x+6)\log _44=\log _420[/tex]
Applying the law that states
[tex]\log _nn=1[/tex]
we have
[tex]\begin{gathered} (x+6)\times1=\log _420 \\ x+6=\log _420 \end{gathered}[/tex]
Collecting like terms, we have
[tex]x=-6+\log _420[/tex]
Therefore, the answer is OPTION C.
