Question

What is the solution to this equation?

log + log 3 =
log(+1)
OA I=
OB.
I=
OC
I=
D. = 1
312
NIT
13

Answer 1

`\textsf{B.} \quad x=(1)/(2)`

Explanation:

Log laws

`\textsf{Product law}: \quad \log_ax + \log_ay=\log_axy`

`\textsf{Equality law}: \quad \textsf{if }\: \log_ax=\log_ay\:\textsf{ then }\:x=y`

Therefore:

`\large \begin{aligned}\log_6 x+ \log_6 3 & =\log_6 (x+1)\\\log_6 (3x) & =\log_6 (x+1)\\3x & =x+1\\2x & =1\\x & =(1)/(2)\end{aligned}`