Question

1. X+10=log3^81. 2. Log9 (2x—8)=4. 3. Log(-2a+9)= log(7–4a)

Answer 1

Answer:

1. $x=-6$

2. $x=\frac{6569}{2}$

3. $a=-1$

Step-by-step explanation:

1. $x+10=\log _3\left(81\right)$

$x+10-10=\log _3\left(81\right)-10$

$x+10-10$

$= x$

$\log _3\left(81\right)-10$

$\log _3\left(81\right)$

$=\log _3\left(3^4\right)$

$=4\log _3\left(3\right)$

$= 4$

$4-10$

$x=-6$

2. $\log _9\left(2x-8\right)=4$

$2x-8=9^4$

$2x-8=6561$

$2x-8+8=6561+8$

$2x=6569$

$\frac{2x}{2}=\frac{6569}{2}$

$x=\frac{6569}{2}$

3. $\log _{10}\left(-2a+9\right)=\log _{10}\left(7-4a\right)$

$-2a+9=7-4a$

$-2a+9-9=7-4a-9$

$-2a=-4a-2$

$-2a+4a=-4a-2+4a$

$2a=-2$

$\frac{2a}{2}=\frac{-2}{2}$

$a=-1$