Question

What is the solution to the equation log(2)x - log(2)4 = 5 ?

Answer 1

\(\log_24 = 2\).
Agree?

Answer 2

yes, thank you!

Answer 3

Nope, not done yet.

\( \color{Black}{\Rightarrow \log_2x - \log_24 = 5 \Longrightarrow \log_2x - 2 = 5}\)

\( \color{Black}{\Rightarrow \log_2x = 7}\)

Answer 4

Can you convert \(\log_2x = 7\) to an exponential form?

Answer 5

Another way to skin the cat is to recognize:
\[\log_{2} x - \log_{2} y = \log_{2}(x / y)\]
So you have \[\log_{2}(x/4) = 5 \rightarrow 2^5 = x/4 \rightarrow 32 = x/4 -> ?\]