Question

How do you solve for log base4 x + log base4 (x+1)=1/2 ???

Answer 1

\(\log_4(x) + \log_4(x+1) = \log_4(x(x+1)) = \log_4(x^2+x)\)
so

\(\log_4(x^2+x) = \frac{1}{2}\implies 4^{\frac{1}{2}}=x^2+x\implies x^2+x-2=0\implies x = -2,1\) but domain of log is positive numbers, so \[x=1\]

Answer 2

thanks(: