Question

Solve the equation

(a) 5(2 − x) ≤ 3x + 2 < 8

(b) 1/8 = 2^3x−4,

(c) log_bx + log_b(x − 4) = log_b21

(d) log₄2x = 2

Answer 1

a)

$10-5x\le3x+2$

$8\le8x$

$1\le\>x$

$3x+2<8$

$3x<6$

$x<2$

$1\le\>x<2$

b)

$2^{-3}=2^{3x-4}$

$-3=3x-4$

$1=3x$

$x=\frac{1}{3}$

c)

Log$_b$ $\begin{bmatrix} x(x-4) \end{bmatrix}=$ log$_b21$

$x^2-4x-21=0$

$x^2-7x+3x-21=0\\ x(x-7)+3(x-7)=0\\(x+3)(x-7)=0\\ x=-3\>or\>7$

d)

$2x=4^2$

$x=8$