Question

How do you solve `log_3 2 + log_3 7 = log_3 x`?

Answer 1

x = 14

Explanation:

Using the `color(blue)"laws of logarithms"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(logx+logy=log(xy))color(white)(a/a)|)))........ (1)`
This law applies to logarithms to any base.

`color(red)(|bar(ul(color(white)(a/a)color(black)(logx=logyrArrx=y)color(white)(a/a)|)))........ (2)`
This law applies to logarithms with equal bases.

Using (1) on left side

`log_3 2+log_3 7=log_3(2xx7)=log_3 14`

Using (2)

`log_3 14=log_3 xrArrx=14`