Question

4^x+2=1/2 solve for x (log equation)

Answer 1

`\log_ab=c\iff a^c=b\\\\4^(x+2)=(1)/(2)\qquad\text{use}\ a^(-1)=(1)/(a)\\\\(2^2)^(x+2)=2^(-1)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\2^(2(x+2))=2^(-1)\iff2(x+2)=-1\qquad\text{use distributive property}\\\\(2)(x)+(2)(2)=-1\\\\2x+4=-1\qquad\text{subtract 4 from both sides}\\\\2x=-3\qquad\text{divide both sides by 2}\\\\\boxed{x=-1.5}`