How do you solve ${log}_{2} (2 x) = {log}_{2} 100$ $log_2(2x)=log_2 100$ ?

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Answer 1 · 2018-07-12T15:28:35

$x = 50$ $color(blue)(x=50)$

If:

${log}_{a} (b) = {log}_{a} (c) \Rightarrow b = c$ $log_a(b)=log_a(c)=>b=c$

Hence:

${log}_{2} (2 x) = {log}_{2} (100)$ $log_2(2x)=log_2(100)$

$2 x = 100 \Rightarrow x = \frac{100}{2} = 50$ $2x=100=>x=100/2=50$

Answer 2 · 2018-07-12T22:07:27

$x = 50$ $x=50$

Since our bases are the same, we can essentially cancel them out and be left with

$2 x = 100$ $2x=100$

By dividing both sides by $2$ $2$ , this easily simplifies to

$x = 50$ $x=50$

Hope this helps!

How do you solve log2(2x)=log2100log_2(2x)=log_2 100?