Intermediate Algebra for College Students (7th Edition)

$x=\frac{4}{3}$
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: $\log x+\log4=\log{(4x)}$ We know that if $a\gt0,a\ne1$, then $\log_ab=\log_ac\longrightarrow b=c$ Thus here: $4x=x+4\\3x=4\\x=\frac{4}{3}$