Video Transcript
Find to the nearest hundredth the value of ๐ฅ for which two to the power of ๐ฅ plus eight equals nine.
Now the first stage to actually solve this equation is take logs of both sides and this gives us log of two to the power of ๐ฅ plus eight equals log of nine. And what we say here by log is log to the base 10. So if we donโt write a base, it automatically means log to the base 10. So if you actually press log in your calculator, then itโs actually gonna calculate as if itโs log to the base 10.
Okay, great, but what do we do now? Well, weโre actually gonna use a log law to help us solve the equation. And the one weโre gonna use is that log ๐ด to the power of ๐ is equal to ๐ log ๐ด. And by applying this law, we get ๐ฅ plus eight log two equals log nine. And we get this because ๐ฅ plus eight was our ๐ and two was our ๐ด.
Okay, great, so now whatโs the next step? Well, the next step is to actually divide each side by log two, which gives us ๐ฅ plus eight is equal to log nine over log two. So then, we actually subtract eight from each side. So therefore, we can say that ๐ฅ is equal to log nine over log two minus eight, which if we put into calculator, we get ๐ฅ is equal to negative 4.8300749986.
So then, we take a look back at the question to see how it wants us to actually leave our answer. And the question says that it wants us to leave it to the nearest hundredth. So therefore, we know that ๐ฅ is equal to negative 4.83.
