[tex]4^{x+3}=6\ \ \ \ |\log_4\\\\\log_44^{x+3}=\log_46\ \ \ |\text{Use}\ \log_ab^n=n\log_ab\\\\(x+3)\log_44=\log_46\ \ \ \ |\text{Use}\ \log_aa=1\\\\x+3=\log_46\ \ \ |-3\\\\x=\log_46-3\ \ \ \ |\text{Use}\ b=\log_aa^b\\\\x=\log_46-\log_44^3\\\\x=\log_46-\log_464\ \ \ |\text{Use}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\x=\log_4\dfrac{6}{64}\\\\x=\log_4\dfrac{3}{32}[/tex]
