Answer:
x = 3/85
Explanation:
log2 (6) - log2 (5x) = log2 ( 34)
We can use the properties of logs.
First subtract log2 (6) from each side.
log2 (6) - log2 (5x) - log2 (6) = log2 ( 34)-log2 (6)
- log2 (5x) = log2 ( 34)-log2 (6)
Now we know that log a - log b = log a/b
- log2 (5x) = log2 ( 34/6)
- log2 (5x) = log2 ( 17/3)
Multiply each side by -1
log2 (5x) = -log2 ( 17/3)
We know that -log (a/b) = log ( b/a)
log2 (5x) = log2 ( 3/17)
The terms inside the logs must be the same
5x = 3/17
Divide each side by 5
5x/5 = 3/17 * 1/5
x = 3/85