Answer
$x=\frac{2}{9}$
Work Step by Step
The product rule for logarithms says that $\log_b{MN}=\log_bM+\log_bN$ i.e. the logarithm of a product is the sum of the logarithms.
The quotient rule for logarithms says that $\log_b{\frac{M}{N}}=\log_bM-\log_bN$ i.e. the logarithm of a quotient is the difference of the logarithms.
The power rule for logarithms says that $\log_b{M^p}=p\log_bM$ i.e. the logarithm of a number with an exponent is the exponent times the logarithm of the number.
$\log_ba=\frac{\log_ca}{\log_cb}$
Hence here: $\log {(x+4)}-\log2=\log{\frac{x+4}{2}}$
We know that if $a\gt0,a\ne1$, then $\log_ab=\log_ac\longrightarrow b=c$
Thus here: $\frac{x+4}{2}=5x+1\\x+4=10x+2\\2=9x\\x=\frac{2}{9}$
But for $x=-8$ both logarithms are undefined, thus there is no solution.
