How do you solve ${log}_{2} (3 x) - {log}_{2} 7 = 3$ $log_2 (3x)-log_2 7=3$ ?

Question

How do you solve ${log}_{2} (3 x) - {log}_{2} 7 = 3$ $log_2 (3x)-log_2 7=3$ ?

1 Answer

Impact of this question

2476 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-08T13:59:47

Use a property of logs to simplify and solve an algebraic equation to get $x = \frac{56}{3}$ $x=56/3$ .

Explanation:

Begin by simplifying ${log}_{2} 3 x - {log}_{2} 7$ $log_2 3x-log_2 7$ using the following property of logs:
$log a - log b = log (\frac{a}{b})$ $loga-logb=log(a/b)$
Note that this property works with logs of every base, including $2$ $2$ .

Therefore, ${log}_{2} 3 x - {log}_{2} 7$ $log_2 3x-log_2 7$ becomes ${log}_{2} (\frac{3 x}{7})$ $log_2 ((3x)/7)$ . The problem now reads:
${log}_{2} (\frac{3 x}{7}) = 3$ $log_2 ((3x)/7)=3$

We want to get rid of the logarithm, and we do that by raising both sides to the power of $2$ $2$ :
${log}_{2} (\frac{3 x}{7}) = 3$ $log_2 ((3x)/7)=3$
$\to 2^{{log}_{2} (\frac{3 x}{7})} = 2^{3}$ $->2^(log_2 ((3x)/7))=2^3$
$\to \frac{3 x}{7} = 8$ $->(3x)/7=8$

Now we just have to solve this equation for $x$ $x$ :
$\frac{3 x}{7} = 8$ $(3x)/7=8$
$\to 3 x = 56$ $->3x=56$
$\to x = \frac{56}{3}$ $->x=56/3$

Since this fraction cannot be simplified further, it is our final answer.

Science

Math

Humanities

... and beyond

How do you solve ${log}_{2} (3 x) - {log}_{2} 7 = 3$ $log_2 (3x)-log_2 7=3$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve log2(3x)−log27=3log_2 (3x)-log_2 7=3?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve ${log}_{2} (3 x) - {log}_{2} 7 = 3$ $log_2 (3x)-log_2 7=3$ ?