Answer
(a) $x=500$
(b) $x=\frac{2}{3}$
(c) $x=3-e^{0.8}$
(d) $x_1=-3$; $x_2=2$
Work Step by Step
Note:
$\log x$ stands for logarithm with base $10$
$\log a+\log b=\log(a\times b)$
---
(a) $\log(2x)=3$
$2x=10^3$
$2x=1000$
$x=500$
(b) $\log(x+1)+\log2=\log(5x)$
$\log((x+1)\times2)=\log(5x)$
$2(x+1)=5x$
$2x+2=5x$
$3x=2$
$x=\frac{2}{3}$
(c) $5\ln(3-x)=4$
$\ln(3-x)=\frac{4}{5}$
$3-x=e^{0.8}$
$x=3-e^{0.8}$
(d) $\log_2(x+2)+\log_2(x-1)=2$
$\log_2(x+2)(x-1)=2$
$(x+2)(x-1)=2^2$
$x^2-x+2x-2=4$
$x^2+x-6=0$
$x_1=-3$; $x_2=2$
