Answer
$x=5$
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: $\log {(2x+3)}+\log2=\log{2(2x+3)}$
We know that if $a\gt0,a\ne1$, then $\log_ab=\log_ac\longrightarrow b=c$
Thus here: $5x+1=2(2x+3)\\5x+1=4x+6\\x+1=6\\x=5$
