Question

Pls Help, Max Points

Answer 1

`\\ \rm\Rrightarrow log_7(5-x)-log_7(3+x)=-1`

• Side change

`\\ \rm\Rrightarrow log_7(5-x)=-1+log_7(3+x)`

• log_a^b+log_a^c=log_^(bc)

`\\ \rm\Rrightarrow 7(5-x)=3+x`

`\\ \rm\Rrightarrow 35-7x=3+x`

`\\ \rm\Rrightarrow 35-3=x+7x`

`\\ \rm\Rrightarrow 32=8x`

`\\ \rm\Rrightarrow x=4`

Answer 2

x = 4

Explanation:

`\large \boxed{\begin{minipage}{7.5 cm}\underline{Log Laws} \\ \\$\textsf{Quotient law}: \quad \log_ax - \log_ay=\log_a(x)/(y) \\ \\\textsf{If }\: \log_ab=c\: \textsf{ then }\: a^c=b$\\\end{minipage}}`

`\large \begin{aligned}\log_7(5-x)-\log_7(3+x) & =-1\\\\\log_7\left((5-x)/(3+x)\right) & =-1\\\\\left((5-x)/(3+x)\right) & =7^(-1)\\\\(5-x)/(3+x) & =(1)/(7)\\\\7(5-x) & =3+x\\\\35-7x & =3+x\\\\35-3 & =x+7x\\\\8x & =32\\\\x & =(32)/(8)\\\\x & =4\end{aligned}`